Question

if ABCD is a rectangle inscribed in a quadrant of a circle of radius 10cm. if AD=2 √5,find the area of the retangle.

Answer 1

The area of the rectangle is 20√19  cm².

Step-by-step explanation:

ABCD is a rectangle inscribed in a quadrant of a circle of radius 10 cm.

Diagonal of rectangle = diameter of circle = 2 x 10 cm = 20 cm

AD = 2√5 cm and BD = 20 cm

By using pythagorean theorem,

AB = $\sqrt{20^{2}-(2\sqrt{5})^{2} }$

AB = $\sqrt{400 - 20}$

AB = √380 cm

Length of the rectangle = L = √380 cm

Width of the rectangle = W = 2√5 cm

Area of the rectangle = LW = √380 x 2√5 = 2√95 x 2 √5 = 4 x 5√19 = 20√19 cm²

Hence, the area of the rectangle is 20√19  cm².