In the following figure, shows a kite in which BCD is the shape of a quadrant of a circle of radius 42 cm. ABCD is a square and Δ CEF is an isosceles right angled triangle whose equal sides are 6 cm long. Find the area of the shaded region.
We will find the area of the shaded region as shown below,
Area of the shaded region = area of quadrant + area of isosceles triangle ……..(1)
$\therefore$ Area of shaded region $=\frac{90}{360} \times \pi \times 42^{2}+\frac{1}{2} \times 6 \times 6$
$\therefore$ Area of shaded region $=\frac{1}{4} \times \pi \times 42^{2}+\frac{1}{2} \times 36$
Substituting $\pi=\frac{22}{7}$ we get,
$\therefore$ Area of shaded region $=\frac{1}{4} \times \frac{22}{7} \times 42^{2}+\frac{1}{2} \times 36$
$\therefore$ Area of shaded region $=\frac{1}{2} \times 11 \times 6 \times 42+18$
$\therefore$ Area of shaded region $=11 \times 3 \times 42+18$
$\therefore$ Area of shaded region $=1386+18$
$\therefore$ Area of shaded region $=1404$
Therefore, area of the shaded region is $1404 \mathrm{~cm}^{2}$.