Question

In the figure, OCDE is a rectangle inscribed in a quadrant of a circle of radius 10 cm. If $DE=2\sqrt{5}$ then find the area of the rectangle.

Answer 1

Radius of the quadrant of circle = 10 cm
$\therefore OD=$ diagonal of rectangle = 10 units
$DE=2\sqrt{5}cm$
$\therefore$ In right $△OED,O{D}^2=O{E}^2+D{E}^2(10{)}^2=O{E}^2+(2\sqrt{5}{)}^{2}100=O{E}^2+20\Rightarrow O{E}^2=100-20=80\Rightarrow O{E}^2=(4\sqrt{5}{)}^2\therefore OE=4\sqrt{5}cm\therefore Areaofrectangle=l\times b=DE\times OE=2\sqrt{5}\times 4\sqrt{5}=8\times 5=40c{m}^2$