Question

In the Figure (i) given below, a square OABC is inscribed in a quadrant OPBQ. If OA = 20 cm, find the area of the shaded region. (Use π = 3.14)

Answer 1

(i) Each side of square OABC = 20 cm. 

∴ OA = 20 cm, AB = 20 cm. 

∴ Area of square PABC = (Side)² 

= (20)² = 400 sq.cm. 

(ii) Diagonal OB is drawn in OABC square. 

In ⊥∆OAB, OA = 20 cm. 

AB = 20 cm. 

OB = ? 

OB² = OA² + AB² 

= (20)² + (20)² 

= 400 + 400 

= 800

∴ Area of shaded region : 

= 628 – 400 

= 228 cm².