"
">

In the figure, $OCDE$ is a rectangle inscribed in a quadrant of a circle of radius $10\ cm$. If $OE = 2\sqrt5$, find the area of the rectangle.
"

Academic Mathematics NCERT Class 9

Given:

$OCDE$ is a rectangle inscribed in a quadrant of a circle of radius $10\ cm$.

$OE = 2\sqrt5$.

To do:

We have to find the area of the rectangle.

Solution:

Radius of the quadrant of the circle $= 2\sqrt5$ units

Diagonal of the rectangle = 10$ units ($OD = OB = OA = 10\ cm$)

$DE = 2\sqrt5\ cm$

In $\triangle OED$,

$OD^2 = OE^2 + DE^2$

$10^2 = OE^2 + (2\sqrt5)^2$

$100 = OE^2 + 20$

$OE^2 = 100 - 20$

$ = 80$

$OE^2 = (4\sqrt5)^2$

$\Rightarrow OE = 4\sqrt5\ cm$

Area of rectangle $= l \times b$

$= DE \times OE$

$= 2\sqrt5 \times 4\sqrt5$

$= 8 \times 5$

$= 40\ cm^2$

The area of the rectangle is $40\ cm^2$.

Updated on: 10-Oct-2022

41 Views

Kickstart Your Career

Get certified by completing the course

Advertisements