Question

find the area of the shaded region.

Answer 1

all three circles are congruent
by const.

P= 90°. (angle in a semi circle )
APQO &BPOR are rhombus (all sides r equal)
Q =90° & R=90° (Angle b/w radius and tangent)
APO & BPO =90° (Angle b/w radius and tangent )
If in a quad . all sides r equal and two angles are 90° then it is a sqaure

hence ,
APQO and BPOR are squares.

area of shaded region = area of semicircle - area of ∆PQR + 2(area of minor segment )
$\frac{\pi \times r {}^{2} }{2} - \frac{1}{2} \times r {}^{2} \times \sin(90) + 2( \frac{90}{360} \times \pi \times r ^{2} - \frac{1}{2} \times r {}^{2} \times \sin(90)$
$\frac{22}{7} - \frac{1}{2} \times 1 \times 1 \times + 2( \frac{1}{4} \times \frac{22}{7} - \frac{1}{2} \times 1 \times 1 \times 1$
$\frac{11}{7} - \frac{1}{2} + ( \frac{11}{7} - \frac{1}{2} )$
$\frac{15}{14} + \frac{15}{14}$
$\frac{30}{14}$
$\frac{15}{7}$
$2.14cm {}^{2}$