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.
Practise Edexcel A Level Maths Radians with exam-style questions for A Level Maths. 52 questions 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, 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.