5.3 Areas of Sectors and Segments

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A design for a decorative stained-glass window panel is shown below. The design consists of a sector $OBC\,$ of a circle with centre $O$ , flanked by two congruent triangles $OAB\,$ and $O D C$ . The point $O\,$ lies on the straight base $A D$ . The points $B\,$ and $C\,$ lie on the arc of the circle. The side lengths $AB\,$ and $DC\,$ are equal, and the angles $\angle AOB\,$ and $\angle DOC\,$ are equal and acute.

Given that:

angle $B O C = 1.8$ radians
area of sector $\text{ cm}^2$
$AOD\,$ is a straight line of length 15.0 cm

Find the radius of the sector, giving your answer in $cm\text{cm}$ to 2 decimal places.

[2]

Find the size of angle $A O B$ , in radians, to 2 decimal places.

[2]

Hence find: the total area of the window panel, giving your answer in $cm2\text{cm}^2$ to one decimal place.

[3]

the total perimeter of the panel, giving your answer in $cm\text{cm}$ to one decimal place.

[3]

5.3 Areas of Sectors and Segments Questions

Practise Edexcel A Level Maths 5.3 Areas of Sectors and Segments with exam-style questions for A Level Maths. 20 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.