In the given figure, ABCD is a rectangle inscribed in a quadrant of a circle of radius 10cm. If AD = 25cm, then area of the rectangle is

Question

In the given figure, ABCD is a rectangle inscribed in a quadrant of a circle of radius 10cm. If AD = 2 5cm, then area of the rectangle is

Philoid · Accepted Answer

Given: ABCD is a rectangle inscribed in a quadrant of a circle of radius 10cm and AD = 25cm

Consider Δ ADC

By Pythagoras theorem

AC² = AD² + DC²

10² = (25)² + AC²

AC² = 10²—(25)²

AC² = 100 – 20 = 80

AC = 45

Area of rectangle = length × breadth = DC × AD

Area of rectangle = 45 × 25 = 40cm²

∴ Area of rectangle = 40cm²