Question

In figure, OCDE is a rectangle inscribed in a quadrant of a circle of radius 10 cm. If OE = 2√5 cm, find the area of the rectangle.

Answer 1

From given: 

Radius = OD = 10 cm and OE = 2√5 cm 

In right ΔDEO, 

By Pythagoras theorem 

OD² = OE² + DE² 

(10)² = (2√5 )² + DE² 

100 – 20 = DE² 

DE = 4√5 

Now, Area of rectangle OCDE = Length x Breadth 

= OE x DE 

= 2√5 x 4√5 

= 40 

Area of rectangle is 40 cm².