Question

Let ABC be a right-angled isosceles triangle with hypotenuse BC. Let BQC be a semi-circle, away from A, with diameter BC. Let BPC be an arc of a circle centered at A and lying between BC and BQC. If AB has length 6 cm then the area, in sq cm, of the region enclosed by BPC and BQC is

• A. $9\pi-18$
• B. 18
• C. $9\pi$
• D. 9

Answer 1

Answer: (B)

18

Answer 2

Let AB =a (where a =6).
CQB is a semicircle with a radius $\frac{a}{\sqrt{2}}$
CPB is a quarter circle (quadrant) with a radius of a.
Therefore, the area of the semicircle is $\frac{\pi a^2}{4}$
Area of quadrant $=\frac{\pi a^2}{4}$
Therefore, the area of the region enclosed by BPC, BQC is equal to the area of triangle ABC, which is 18.