A design for a decorative stained-glass window panel is shown below. The design consists of a sector OBC OBC\,OBC of a circle with centre OOO, flanked by two congruent triangles OAB OAB\,OAB and ODCODCODC. The point O O\,O lies on the straight base ADADAD. The points B B\,B and C C\,C lie on the arc of the circle. The side lengths AB AB\,AB and DC DC\,DC are equal, and the angles ∠AOB \angle AOB\,∠AOB and ∠DOC \angle DOC\,∠DOC are equal and acute.
Given that:
Find the radius of the sector, giving your answer in cm\text{cm}cm to 2 decimal places.
Find the size of angle AOBAOBAOB, in radians, to 2 decimal places.
Hence find: the total area of the window panel, giving your answer in cm2\text{cm}^2cm2 to one decimal place.
the total perimeter of the panel, giving your answer in cm\text{cm}cm 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.