The Total solution for NCERT class 6-12
In Fig. 12.31, asquare OABC is inscribed in a quadrant OPBQ. If OA = 20 cm, find the area ofthe shaded region. (Use ╧А = 3.14)
Solution:
Side of square = OA = AB = 20 cm
Radius of the quadrant = OB
OAB is right angled triangle
By Pythagoras theorem in ╬ФOAB,
OB2┬а= AB2+OA2
тЗТ OB2┬а= 202┬а+202
тЗТ OB2┬а= 400+400
тЗТ OB2┬а= 800
тЗТ OB= 20тИЪ2 cm
Area of the quadrant = (╧АR2)/4 cm2┬а=(3.14/4)├Ч(20тИЪ2)2┬аcm2┬а= 628cm2
Area of the square = 20├Ч20 = 400 cm2
Area of the shaded region = Area of thequadrant тАУ Area of the square
= 628-400 cm2┬а= 228cm2