Question

in the fig given above , a square oabc is inscribed in quadrant opbq of a circle. if oa=20cm, find the area of shaded portion.

Answer 1

Radius of Quadrant = OB

Therefore  

$\bf\huge OB = \sqrt{(OA)^2 + (AB)^2}$

$\bf\huge OB = \sqrt{(20)^2 + (20)^2}$

$\bf\huge 20 \sqrt{1 + 1}$

$\bf\huge 20 \sqrt{2}$

Area of Quadrant OPBQ

$\bf\huge\frac{1}{4}pie r^2$

$\bf\huge\frac{1}{4}\times 3.14\times (20 \sqrt{2})^2$

$\bf\huge\frac{1}{4}\times 3.14\times 800 = 628$

Area of Square OABC

=> 20^2 = 400

Area of Shaded region

= Area of Quadrant - Area of Square OABC

= (628 - 400)

= 228 cm