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

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

#### Solution

Given OD = 10cm and OE   root (2)(5)cm

By using Pythagoras theorem

∴ OD^2 = OE^2 + DE^2

⇒ DE = sqrt( OD^2 - OF^2) =  sqrt (( 10 )^2 - (root2(5)))^2 = root 4 (5)cm

∴ ar (rect DCDE) = OExx DE = root2( 5) xx root 4 (5 )cm^2

= 40 cm^ 2              [ ∴ sqrt5 xx sqrt 5  = 5]

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#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 14 Areas of Parallelograms and Triangles
Exercise 14.3 | Q 6 | Page 45