# PQRS is a rectangle inscribed in a quadrant of a circle of radius 13 cm. A is any point on PQ. If PS = 5 cm, then find ar (ΔRAS) - Mathematics

PQRS is a rectangle inscribed in a quadrant of a circle of radius 13 cm. A is any point on PQ. If PS = 5 cm, then find ar (ΔRAS)

#### Solution

Given: Here from the given figure we get

(1) PQRS is a rectangle inscribed in a quadrant of a circle with radius 10cm,

(2) PS = 5cm

To find: Area of ΔRAS.

Calculation: In right ΔPSR, (Using Pythagoras Theorem)

PR^2 = PS^2 + SR^2

13^2 = 5^2 + SR^2

SR^2 = 13^2 - 5^2

SR^2 = 169-25

SR^2 = 144

SR = 12 cm

Area of Δ = 1/2 base × height

Area of ΔRAS = 1/2  × base × height

= 1/2  × RS × SP

= 1/2 × 12 × 5

=1/2 × 60

Area of ΔRAS = 30 cm

Hence we get the Area of ΔRAS = 30 cm2

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#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 14 Areas of Parallelograms and Triangles
Q 5 | Page 60