Question

find the area of shaded region​

Answer 1

In the given figure, the hypotenuse of the right triangle is the diameter of the circle since diameter subtends a right angle on the circumference.

so,

we know that

(hypotenuse)² = (base)² + (perpendicular)²

d² = 7² + 7²

d² = 49 + 49

d² = 2x49

d = √(2x49)

d = √(2 x 7²)

d = 7√2 cm

r = d/2 = (7√2)/2

now, area of the shaded region

= ar(semicircle) - ar(triangle)

$= \frac{1}{2} \pi \: {r}^{2} - \frac{1}{2} \times b \times h \\ = \frac{1}{2} \times \frac{22}{7} \times {( \frac{7 \sqrt{2} }{2} )}^{2} - (\frac{1}{2} \times 7 \times 7 )\\ = \frac{1}{2} \times \frac{22}{7} \times \frac{98}{4} - ( \frac{49}{2} ) \\ = \frac{1}{1} \times \frac{11}{7} \times \frac{49}{2} - \frac{49}{2} \\ = \frac{49}{2} \times \frac{11}{7} - \frac{49}{2} \\ = \frac{49}{2} ( \frac{11}{7} - 1) = \frac{49}{2} ( \frac{11 - 7}{7} ) \\ = \frac{49}{2} \times \frac{4}{7} = \frac{7}{1} \times \frac{2}{1} \\ = 14 \: {cm}^{2}$

Hence, area of the shaded region is 14 cm²