Find the easiest solution of ncert class 10 areas related to circle . Sir please help me to solve the exercise 12.3 question no.13 Give me the best solution of this question its very important question of this chapter.In Fig. 12.31, a square OABC is inscribed in a quadrant OPBQ. If OA = 20 cm, find the area of the shaded region. (Use π = 3.14).
Side of square = OA = AB = 20 cm
Radius of the quadrant = OB
OAB is right angled triangle
By Pythagoras theorem in ΔOAB,
OB2 = AB2+OA2
⇒ OB2 = 202 +202
⇒ OB2 = 400+400
⇒ OB2 = 800
⇒ OB= 20√2 cm
Area of the quadrant = (πR2)/4 cm2 = (3.14/4)×(20√2)2 cm2 = 628cm2
Area of the square = 20×20 = 400 cm2
Area of the shaded region = Area of the quadrant – Area of the square
= 628-400 cm2 = 228cm2