The boundary of a circular wildlife sanctuary is modeled by the equation x2+y2−14x+8y=175x^2 + y^2 - 14x + 8y = 175x2+y2−14x+8y=175, where distances are measured in kilometers.
A straight firebreak path connects two points A A\,A and B B\,B on the boundary. The angle subtended by the arc AB AB\,AB at the center of the sanctuary is 1.4 radians.
Calculate the area of the region bounded by the arc AB AB\,AB and the straight path ABABAB (the minor segment).
Give your answer to three significant figures.
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.