A designer is creating a custom metal plate in the shape of a logo, PQRSPPQRS PPQRSP. The logo consists of a major sector PQROPQROPQRO of a circle with centre OOO and radius 12 cm12\text{ cm}12 cm, joined to a triangle POSPOSPOS. The point SSS lies on the radius OROROR. The length of the straight edge PSPSPS is 10 cm10\text{ cm}10 cm and the angle POSPOSPOS is 0.75 radians0.75\text{ radians}0.75 radians.
Find the area of the major sector PQROPQROPQRO, giving your answer to one decimal place.
Given that the angle PSOPSOPSO is obtuse,
find the size of angle PSOPSOPSO in radians, giving your answer to 3 decimal places.
Determine the total perimeter of the shape PQRSPPQRS PPQRSP, giving your answer to one decimal place.
69 exam-style questions on Edexcel A Level Maths Radians, covering 5.1 Radian Measure, 5.2 Arc Length, 5.3 Areas of Sectors and Segments, 5.4 Solving Trigonometric Equations, and 5.5 Small Angle Approximations. Each one has a worked solution and a mark scheme showing where the marks go.