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Area: the amount of flat space inside a shape.
Perimeter: the total distance around the outside edge.

","mcqOptions":[{"text":"

Area: the amount of flat space inside a shape.
Perimeter: the total distance around the outside edge.

","correct":true,"explanation":"Area describes the surface enclosed by a shape, while perimeter measures the complete distance around its boundary. They use different units: square units for area and length units for perimeter."},{"text":"

Area: the total distance around the outside edge.
Perimeter: the amount of flat space inside a shape.

","correct":false,"explanation":"The two definitions have been reversed, a common confusion between what is inside a shape and what goes around its boundary. Area is the inside space, while perimeter is the outside distance."},{"text":"

Area: the longest distance across a shape.
Perimeter: the amount of flat space inside a shape.

","correct":false,"explanation":"The longest distance across a shape is a measurement such as a diagonal, not area. Area measures inside space, while perimeter measures the total distance around the outside edge."},{"text":"

Area: the total distance around the outside edge.
Perimeter: the longest distance across a shape.

","correct":false,"explanation":"This confuses both concepts with other measurements. Area is the flat space inside a shape, and perimeter is found by adding all the lengths around its outside edge."}]},{"id":"65fd431f-9353-49b1-b2ce-02b2251c4bad","cardType":"cloze","points":null,"front":"Area is measured in [ ] (e.g. cm²), while perimeter is measured in length units (e.g. cm).","back":"Area is measured in square units (e.g. cm²), while perimeter is measured in length units (e.g. cm).","mcqOptions":[{"text":"square units","correct":true,"explanation":"Area measures the amount of two-dimensional space covered by a shape, so its units have two dimensions, such as cm². These are called square units."},{"text":"length units","correct":false,"explanation":"Length units such as centimetres measure one-dimensional distance and are used for perimeter. Area requires square units, such as cm², because it covers a surface."},{"text":"cubic units","correct":false,"explanation":"Cubic units measure volume in three dimensions, such as cm³. Area is two-dimensional, so it is measured in square units such as cm²."},{"text":"angle units","correct":false,"explanation":"Angle units such as degrees measure rotation or the size of an angle, not surface space. Area is measured in square units, such as cm²."}]},{"id":"9f1e2b2e-4385-491f-9998-e5505a33125c","cardType":"cloze","points":null,"front":"Area is measured in square units (e.g. cm²), while perimeter is measured in [ ] (e.g. cm).","back":"Area is measured in square units (e.g. cm²), while perimeter is measured in length units (e.g. cm).","mcqOptions":[{"text":"length units","correct":true,"explanation":"Perimeter measures the total distance around a shape, which is one-dimensional. Therefore it uses ordinary length units, such as centimetres, rather than square or cubic units."},{"text":"square units","correct":false,"explanation":"Square units measure two-dimensional area, not the one-dimensional distance around a boundary. Perimeter is measured in length units such as cm."},{"text":"cubic units","correct":false,"explanation":"Cubic units measure three-dimensional volume and are unsuitable for a boundary distance. Perimeter uses length units, such as cm, because it measures distance in one dimension."},{"text":"angle units","correct":false,"explanation":"Angle units measure turns or angles, not distances. The perimeter of a shape is the total length around its edge, so it is measured in length units such as cm."}]},{"id":"e772ff5c-da12-45d8-9da3-af9ef435a9c1","cardType":"basic","points":1,"front":"What is the formula for the area of a rectangle?","back":"$$A = l \\times w$ (length multiplied by width).","mcqOptions":[{"text":"$$A = l \\times w$ (length multiplied by width).","correct":true,"explanation":"A rectangle’s area is found by multiplying its length by its width, so the formula is $A = l \\times w$. Both measurements must use compatible length units."},{"text":"$$A = 2l + 2w$ (twice the length plus twice the width).","correct":false,"explanation":"This formula adds all four sides, so it finds the rectangle’s perimeter rather than its area. Area requires multiplication: $A = l \\times w$."},{"text":"$$A = l + w$ (length plus width).","correct":false,"explanation":"Adding the length and width does not cover the rectangle’s surface and is not an area formula. The correct calculation multiplies them: $A = l \\times w$."},{"text":"$$A = l \\div w$ (length divided by width).","correct":false,"explanation":"Dividing the dimensions does not calculate the rectangular surface and can also produce unsuitable units. Multiply length by width to find area: $A = l \\times w$."}]},{"id":"943d5a6f-156d-4d29-a562-8c87c659a2f0","cardType":"basic","points":1,"front":"What is the formula for the perimeter of a rectangle?","back":"$$P = 2l + 2w$ (or $P = 2(l + w)$).","mcqOptions":[{"text":"$$P = 2l + 2w$ (or $P = 2(l + w)$).","correct":true,"explanation":"A rectangle has two sides of length $l$ and two sides of width $w$, so its perimeter is $2l + 2w$, equivalently $2(l + w)$."},{"text":"$$P = l + w$ (length plus width).","correct":false,"explanation":"This adds only one length and one width, omitting the opposite sides. A rectangle’s perimeter includes two of each, so $P = 2l + 2w$."},{"text":"$$P = l \\times w$ (length multiplied by width).","correct":false,"explanation":"Multiplying length by width calculates the rectangle’s area, not the distance around it. The perimeter formula adds both pairs of equal sides: $P = 2l + 2w$."},{"text":"$$P = 2l + w$ (twice the length plus the width).","correct":false,"explanation":"This includes two lengths but only one width, so one side is missing from the boundary total. The correct formula includes two widths as well: $P = 2l + 2w$."}]},{"id":"2ba0ef39-b7b9-43e0-87f8-2c6c9a0c4c14","cardType":"basic","points":1,"front":"How do you find the side length of a square if you know its area?","back":"Calculate the square root of the area ($\\sqrt{A}$).","mcqOptions":[{"text":"Calculate the square root of the area ($\\sqrt{A}$).","correct":true,"explanation":"For a square, area equals side length squared, $A=s^2$. Taking the square root reverses the squaring operation, giving the side length as $s=\\sqrt{A}$."},{"text":"Calculate the square of the area ($A^2$).","correct":false,"explanation":"Squaring the area moves further away from the side length and produces incorrect units. Since $A=s^2$, take the square root to obtain $s=\\sqrt{A}$."},{"text":"Calculate half of the area ($A \\div 2$).","correct":false,"explanation":"Halving the area has no general connection with a square’s side length. The side is the number which squares to give the area, so use $\\sqrt{A}$."},{"text":"Calculate the cube root of the area ($\\sqrt[3]{A}$).","correct":false,"explanation":"A cube root reverses cubing and is associated with three-dimensional volume, not the area of a square. Square area requires the square root, $\\sqrt{A}$."}]},{"id":"cc65cb64-afbd-43fb-b7a7-040a34a047f5","cardType":"basic","points":2,"front":"A square has area 81 cm². What is its perimeter?","back":"

Find side length: $\\sqrt{81} = 9$ cm.
Multiply by 4: $9 \\times 4 = 36$ cm.

","mcqOptions":[{"text":"

Find side length: $\\sqrt{81} = 9$ cm.
Multiply by 4: $9 \\times 4 = 36$ cm.

","correct":true,"explanation":"The side length of a square is the square root of its area, so $\\sqrt{81}=9$ cm. A square has four equal sides, giving a perimeter of $4 \\times 9=36$ cm."},{"text":"

Find side length: $81 \\div 4 = 20.25$ cm.
Multiply by 4: $20.25 \\times 4 = 81$ cm.

","correct":false,"explanation":"Dividing the area by four treats the area as though it were a perimeter. The side length comes from $\\sqrt{81}=9$ cm, so the perimeter is $4 \\times 9=36$ cm."},{"text":"

Find side length: $\\sqrt{81} = 9$ cm.
Multiply by 2: $9 \\times 2 = 18$ cm.

","correct":false,"explanation":"The square root correctly finds the side, but multiplying by two counts only a pair of sides. A square has four equal sides, so the perimeter is $9 \\times 4=36$ cm."},{"text":"

Find side length: $81$ cm.
Multiply by 4: $81 \\times 4 = 324$ cm.

","correct":false,"explanation":"The area value is not itself the side length; confusing these gives an excessively large perimeter. The side is $\\sqrt{81}=9$ cm, making the perimeter $36$ cm."}]},{"id":"669d1b1c-ed24-4e89-8b18-f69a6073cf67","cardType":"basic","points":2,"front":"A square has perimeter 32 cm. What is its area?","back":"

Find side length: $32 \\div 4 = 8$ cm.
Square the side: $8^2 = 64$ cm².

","mcqOptions":[{"text":"

Find side length: $32 \\div 4 = 8$ cm.
Square the side: $8^2 = 64$ cm².

","correct":true,"explanation":"A square’s four equal sides give a side length of $32 \\div 4=8$ cm. Squaring this side gives the area: $8^2=64$ cm²."},{"text":"

Find side length: $32 \\div 4 = 8$ cm.
Multiply the side by 4: $8 \\times 4 = 32$ cm².

","correct":false,"explanation":"The side length is found correctly, but multiplying by four returns the perimeter rather than the area. Area requires squaring the side, so $8^2=64$ cm²."},{"text":"

Find side length: $32 \\div 2 = 16$ cm.
Square the side: $16^2 = 256$ cm².

","correct":false,"explanation":"Dividing the perimeter by two counts two sides instead of all four, making the side twice as large. Use $32 \\div 4=8$ cm, then square to get $64$ cm²."},{"text":"

Find side length: $\\sqrt{32}$ cm.
Square the side: $(\\sqrt{32})^2 = 32$ cm².

","correct":false,"explanation":"Taking a square root is used when area is known and the side is required. Here the perimeter gives the side as $32 \\div 4=8$ cm, producing an area of $64$ cm²."}]},{"id":"dcdef895-f131-4c98-9d84-8adbd53b6b12","cardType":"basic","points":2,"front":"If the length of a rectangle is twice its width ($w$), what is the expression for its perimeter?","back":"$$6w$ (from $w + w + 2w + 2w$).","mcqOptions":[{"text":"$$6w$ (from $w + w + 2w + 2w$).","correct":true,"explanation":"The two widths total $2w$ and the two lengths total $4w$, so the perimeter is $2w + 4w = 6w$."},{"text":"$$4w$ (from $w + w + w + w$).","correct":false,"explanation":"This treats all four sides as width $w$, ignoring that each length is $2w$. Adding $w + w + 2w + 2w$ gives the correct perimeter, $6w$."},{"text":"$$3w$ (from $w + 2w$).","correct":false,"explanation":"This adds only one width and one length, giving half the perimeter. A rectangle has two of each side, so the correct perimeter is $2(w + 2w) = 6w$."},{"text":"$$2w^2$ (from $2w \\times w$).","correct":false,"explanation":"Multiplying length by width calculates the area, not the perimeter. Perimeter requires adding all four sides, which gives $w + w + 2w + 2w = 6w$."}]},{"id":"07813d35-f424-4af2-bf39-970388a962dc","cardType":"basic","points":1,"front":"If the length of a rectangle is three times its width ($w$), what is the expression for its area?","back":"$$3w^2$ (from $3w \\times w$).","mcqOptions":[{"text":"$$3w^2$ (from $3w \\times w$).","correct":true,"explanation":"A rectangle’s area is length multiplied by width. With length $3w$ and width $w$, the area is $3w \\times w = 3w^2$."},{"text":"$$8w$ (from $w + w + 3w + 3w$).","correct":false,"explanation":"Adding all four sides calculates the perimeter rather than the area. Multiplying the length $3w$ by the width $w$ gives the correct area, $3w^2$."},{"text":"$$4w^2$ (from $(3w + w) \\times w$).","correct":false,"explanation":"This incorrectly adds the length and width before multiplying. Rectangle area is simply length multiplied by width, so $3w \\times w = 3w^2$."},{"text":"$$9w^2$ (from $3w \\times 3w$).","correct":false,"explanation":"This uses $3w$ for both dimensions, incorrectly treating the rectangle as a square. Its width is $w$, so the area is $3w \\times w = 3w^2$."}]},{"id":"84e5a3ae-2513-417d-b3c9-fcdc7c52015f","cardType":"basic","points":1,"front":"What is the formula for the area of a triangle?","back":"$$A = \\frac{1}{2}bh$ (half $\\times$ base $\\times$ perpendicular height).","mcqOptions":[{"text":"$$A = \\frac{1}{2}bh$ (half $\\times$ base $\\times$ perpendicular height).","correct":true,"explanation":"A triangle occupies half the area of a parallelogram with the same base and perpendicular height. Therefore its area is $A = \\frac{1}{2}bh$."},{"text":"$$A = bh$ (base $\\times$ perpendicular height).","correct":false,"explanation":"This is the area formula for a parallelogram and misses the factor of one-half. A triangle’s area is $A = \\frac{1}{2}bh$, using its perpendicular height."},{"text":"$$A = \\frac{1}{2}(b + h)$ (half $\\times$ base plus height).","correct":false,"explanation":"Adding the base and height cannot produce an area because it does not create squared units. The dimensions must be multiplied, giving $A = \\frac{1}{2}bh$."},{"text":"$$A = \\frac{1}{2}b^2$ (half $\\times$ base $\\times$ base).","correct":false,"explanation":"This incorrectly uses the base twice and ignores the perpendicular height. Triangle area depends on both measurements, so the correct formula is $A = \\frac{1}{2}bh$."}]},{"id":"dd2d156a-bf71-4b85-9fff-3c893e03cfd5","cardType":"cloze","points":null,"front":"For triangles and parallelograms, the height used in area formulas must be [ ] to the base, never the slanted side.","back":"For triangles and parallelograms, the height used in area formulas must be perpendicular to the base, never the slanted side.","mcqOptions":[{"text":"perpendicular","correct":true,"explanation":"The height is the shortest distance from the base to the opposite vertex or side, measured at a right angle. Therefore it must be perpendicular to the base."},{"text":"parallel","correct":false,"explanation":"A parallel line never meets the base, so it cannot represent the height between the base and the opposite vertex or side. The required height is perpendicular to the base."},{"text":"diagonal","correct":false,"explanation":"A diagonal joins non-adjacent vertices and is not necessarily at a right angle to the base. Area formulas require the perpendicular distance from the base."},{"text":"adjacent","correct":false,"explanation":"An adjacent side may be slanted and therefore may not measure the shortest distance from the base. The height used for area must be perpendicular to the base."}]},{"id":"00ae11c0-7627-4bdc-804f-1ee829dba678","cardType":"cloze","points":null,"front":"For triangles and parallelograms, the height used in area formulas must be perpendicular to the base, never the [ ] side.","back":"For triangles and parallelograms, the height used in area formulas must be perpendicular to the base, never the slanted side.","mcqOptions":[{"text":"slanted","correct":true,"explanation":"A slanted side is not generally perpendicular to the base, so using it would give an incorrect area. The height must be the right-angled distance from the base."},{"text":"parallel","correct":false,"explanation":"The warning concerns a visible side that learners often mistake for the height, namely the slanted side. A parallel side is not a candidate for the perpendicular height."},{"text":"horizontal","correct":false,"explanation":"Whether a side is horizontal depends only on how the shape is drawn, not on its role in the formula. The side to avoid using as height is the slanted side."},{"text":"opposite","correct":false,"explanation":"In a parallelogram, the opposite side is parallel to the chosen base and helps define the shape. The common error is using the slanted side instead of perpendicular height."}]},{"id":"4c2795f4-59c3-4034-ad9d-54b375b4efb1","cardType":"basic","points":1,"front":"What is the formula for the area of a parallelogram?","back":"$$A = bh$ (base $\\times$ perpendicular height).","mcqOptions":[{"text":"$$A = bh$ (base $\\times$ perpendicular height).","correct":true,"explanation":"A parallelogram can be rearranged into a rectangle with the same base and perpendicular height. Its area is therefore $A = bh$."},{"text":"$$A = \\frac{1}{2}bh$ (half $\\times$ base $\\times$ perpendicular height).","correct":false,"explanation":"The factor of one-half belongs to the triangle area formula. A parallelogram uses the full product of its base and perpendicular height, so $A = bh$."},{"text":"$$A = bs$ (base $\\times$ slanted side).","correct":false,"explanation":"The slanted side does not measure the perpendicular distance between the parallel bases. The area must use perpendicular height, giving $A = bh$."},{"text":"$$A = 2(b + h)$ (twice base plus height).","correct":false,"explanation":"This resembles a perimeter calculation because it adds lengths rather than multiplying dimensions. Parallelogram area is base multiplied by perpendicular height, so $A = bh$."}]},{"id":"f3160eb4-827b-4ec7-9d3c-32a1d04fd949","cardType":"basic","points":3,"front":"A triangle has area 25 cm² and the base is twice the height ($2h$). Find the height.","back":"

Substitute: $25 = \\frac{1}{2} \\times 2h \\times h$.
Simplify: $25 = h^2$.
Solve: $h = 5$ cm.

","mcqOptions":[{"text":"

Substitute: $25 = \\frac{1}{2} \\times 2h \\times h$.
Simplify: $25 = h^2$.
Solve: $h = 5$ cm.

","correct":true,"explanation":"Substituting base $2h$ into $A = \\frac{1}{2}bh$ gives $25 = h^2$. Taking the positive square root gives $h = 5$ cm, since height cannot be negative."},{"text":"

Substitute: $25 = \\frac{1}{2} \\times 2h \\times h$.
Simplify: $25 = 2h^2$.
Solve: $h = 3.54$ cm.

","correct":false,"explanation":"This fails to cancel $\\frac{1}{2}$ with the factor $2$ in the base. The equation simplifies to $25 = h^2$, so the height is $5$ cm."},{"text":"

Substitute: $25 = 2h \\times h$.
Simplify: $25 = 2h^2$.
Solve: $h = 3.54$ cm.

","correct":false,"explanation":"This uses the rectangle or parallelogram formula and omits the triangle’s factor of $\\frac{1}{2}$. Correct substitution gives $25 = \\frac{1}{2}(2h)(h) = h^2$, hence $h = 5$ cm."},{"text":"

Substitute: $25 = \\frac{1}{2} \\times 2h \\times h$.
Simplify: $25 = h^2$.
Solve: $h = 12.5$ cm.

","correct":false,"explanation":"This divides $25$ by $2$ instead of taking the square root when solving $h^2 = 25$. The positive square root gives the correct height, $h = 5$ cm."}]},{"id":"2df363c4-c1f6-4de2-a955-2c225534698a","cardType":"basic","points":1,"front":"What are the geometric properties of a parallelogram?","back":"A four-sided shape with two pairs of parallel opposite sides.","mcqOptions":[{"text":"A four-sided shape with two pairs of parallel opposite sides.","correct":true,"explanation":"A parallelogram is a quadrilateral whose two pairs of opposite sides are parallel. This defining property also leads to equal opposite sides and equal opposite angles."},{"text":"A four-sided shape with one pair of parallel opposite sides.","correct":false,"explanation":"Having only one pair of parallel opposite sides describes a trapezium in UK terminology. A parallelogram must have two pairs of parallel opposite sides."},{"text":"A four-sided shape with two pairs of perpendicular opposite sides.","correct":false,"explanation":"Opposite sides cannot be perpendicular because they face each other rather than meeting. In a parallelogram, both pairs of opposite sides are parallel."},{"text":"A four-sided shape with four pairs of parallel opposite sides.","correct":false,"explanation":"A quadrilateral has only two pairs of opposite sides, so four such pairs are impossible. A parallelogram is defined by two pairs of parallel opposite sides."}]},{"id":"2d045577-f2ac-403c-a5a3-9da0adb840f5","cardType":"basic","points":1,"front":"What is the formula for the area of a trapezium?","back":"$$A = \\frac{1}{2}(a+b)h$","mcqOptions":[{"text":"$$A = \\frac{1}{2}(a+b)h$","correct":true,"explanation":"The parallel side lengths are added, multiplied by the perpendicular height, and halved. This is equivalent to multiplying the average length of the parallel sides by the height."},{"text":"$$A = (a+b)h$","correct":false,"explanation":"Omitting the factor of $\\frac{1}{2}$ doubles the calculated area. The correct formula uses the average of the parallel sides: $A = \\frac{1}{2}(a+b)h$."},{"text":"$$A = \\frac{1}{2}(a-b)h$","correct":false,"explanation":"Subtracting the parallel sides does not find their average and can even produce a negative result. They must be added, giving $A = \\frac{1}{2}(a+b)h$."},{"text":"$$A = \\frac{1}{2}abh$","correct":false,"explanation":"Multiplying the two parallel side lengths together incorrectly treats the trapezium like a three-dimensional calculation. The correct formula is $A = \\frac{1}{2}(a+b)h$."}]},{"id":"6200049b-51d8-4f77-a768-8d62118a7a49","cardType":"basic","points":1,"front":"In the trapezium formula $A = \\frac{1}{2}(a+b)h$, what do $a$ and $b$ represent?","back":"The lengths of the parallel sides.","mcqOptions":[{"text":"The lengths of the parallel sides.","correct":true,"explanation":"The variables $a$ and $b$ are the two parallel side lengths. Their mean is multiplied by the perpendicular height $h$ to calculate the trapezium’s area."},{"text":"The lengths of the non-parallel sides.","correct":false,"explanation":"The sloping or non-parallel sides are not added in the area formula. The variables $a$ and $b$ represent the lengths of the parallel sides."},{"text":"The length and the perpendicular height.","correct":false,"explanation":"The perpendicular height is represented separately by $h$, not by $a$ or $b$. Both $a$ and $b$ are lengths of the parallel sides."},{"text":"The lengths of the two diagonals.","correct":false,"explanation":"A trapezium’s diagonals are not used in this area formula. The variables $a$ and $b$ represent the lengths of its two parallel sides."}]},{"id":"6ff4d787-aa05-465f-8667-314752cd1785","cardType":"basic","points":3,"front":"What three steps are used to calculate trapezium area?","back":"

Add the parallel sides.
Halve the result.
Multiply by the perpendicular height.

","mcqOptions":[{"text":"

Add the parallel sides.
Halve the result.
Multiply by the perpendicular height.

","correct":true,"explanation":"These steps apply $A = \\frac{1}{2}(a+b)h$: add the parallel side lengths, divide their sum by two, then multiply by the perpendicular height."},{"text":"

Subtract the parallel sides.
Halve the result.
Multiply by the perpendicular height.

","correct":false,"explanation":"Subtracting the parallel sides finds their difference rather than their average. They must be added, the sum halved, and the result multiplied by the perpendicular height."},{"text":"

Add the parallel sides.
Double the result.
Multiply by the perpendicular height.

","correct":false,"explanation":"Doubling instead of halving makes the answer four times the correct area. Add the parallel sides, halve their sum, then multiply by the perpendicular height."},{"text":"

Add the non-parallel sides.
Halve the result.
Multiply by the perpendicular height.

","correct":false,"explanation":"The area formula uses the parallel sides, not the sloping or non-parallel sides. Add the parallel sides, halve the sum, then multiply by the perpendicular height."}]},{"id":"a067146d-ae0b-450a-bf04-b0966eb50600","cardType":"cloze","points":null,"front":"A trapezium is a four-sided shape with exactly [ ] of parallel sides.","back":"A trapezium is a four-sided shape with exactly one pair of parallel sides.","mcqOptions":[{"text":"one pair","correct":true,"explanation":"Under the definition used here, a trapezium is a quadrilateral with exactly one pair of parallel sides. The other pair of opposite sides is not parallel."},{"text":"two pairs","correct":false,"explanation":"A quadrilateral with two pairs of parallel sides is a parallelogram, with rectangles, rhombuses and squares as special cases. A trapezium has exactly one pair."},{"text":"no pairs","correct":false,"explanation":"A quadrilateral with no parallel sides does not meet the definition of a trapezium used here. A trapezium must have exactly one pair of parallel sides."},{"text":"three pairs","correct":false,"explanation":"A four-sided polygon has only two pairs of opposite sides, so it cannot have three pairs of parallel sides. A trapezium has exactly one pair."}]},{"id":"c508cb3b-9986-4c10-9917-2aa3749d38c5","cardType":"basic","points":2,"front":"When calculating the perimeter of a compound shape, which edges are ignored?","back":"Any joined edges inside the shape; only the outside boundary is counted.","mcqOptions":[{"text":"Any joined edges inside the shape; only the outside boundary is counted.","correct":true,"explanation":"Perimeter is the total distance around a shape’s exterior. Edges where component shapes join are internal, so they do not form part of the outside boundary."},{"text":"Any curved edges inside the shape; only the straight boundary is counted.","correct":false,"explanation":"Curved exterior edges still contribute to perimeter; being curved does not exclude them. Only joined edges inside the compound shape are ignored, while the entire outside boundary is counted."},{"text":"Any short edges inside the shape; only the longest boundary is counted.","correct":false,"explanation":"Edge length does not determine whether an edge contributes to perimeter. Every outside edge is counted, while joined edges inside the compound shape are ignored."},{"text":"Any outside edges around the shape; only the joined boundary is counted.","correct":false,"explanation":"This reverses the perimeter rule by counting internal joins instead of the exterior. Joined edges inside are ignored, and only the outside boundary is included."}]},{"id":"bc457ba3-6066-48d2-af1f-e50f62d4bfc9","cardType":"cloze","points":null,"front":"A square with side $s$ has area $\\text{[...]}$ and perimeter $4s$.","back":"A square with side $s$ has area $\\boxed{s^2}$ and perimeter $4s$.","mcqOptions":[{"text":"$$s^2$","correct":true,"explanation":"A square’s area is length multiplied by width. Both dimensions equal $s$, so its area is $s \\times s = s^2$."},{"text":"$$s$","correct":false,"explanation":"Using $s$ alone gives a length rather than an area and misses the second dimension. Multiplying the two equal side lengths gives the correct area, $s^2$."},{"text":"$$2s$","correct":false,"explanation":"Adding two side lengths gives neither the square’s area nor its full perimeter. Area requires multiplication of the dimensions, so it is $s \\times s = s^2$."},{"text":"$$4s^2$","correct":false,"explanation":"Multiplying $s^2$ by four incorrectly treats the square as four separate regions of area $s^2$. The whole square’s area is simply $s^2$."}]},{"id":"1fa77e05-6679-482d-88a3-47735c730766","cardType":"cloze","points":null,"front":"A square with side $s$ has area $s^2$ and perimeter $\\text{[...]}$.","back":"A square with side $s$ has area $s^2$ and perimeter $\\boxed{4s}$.","mcqOptions":[{"text":"$$4s$","correct":true,"explanation":"A square has four equal sides, each of length $s$. Adding them gives $s+s+s+s=4s$, so the perimeter is $4s$."},{"text":"$$s^2$","correct":false,"explanation":"Squaring the side length calculates the square’s area, not the distance around it. Adding its four equal sides gives the correct perimeter, $4s$."},{"text":"$$2s$","correct":false,"explanation":"Multiplying by two counts only two of the square’s four equal sides. The perimeter includes every side, so it is $4s$."},{"text":"$$8s$","correct":false,"explanation":"Multiplying by eight double-counts each of the square’s four sides. Each side is included once, giving the correct perimeter of $4s$."}]}]}],"examCountdown":null,"heading":"Area and Perimeter","title":"Area and Perimeter Flashcards","topbar":{"backHref":"/igcse/maths/cie/flashcards"},"topicSidebar":"$L38"}]}],"topicId":"c17e2b59-b879-4f79-b7da-be901e20f072","walled":"$L39"}],"$L3a","$L3b"]