Question

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) 

Answer 1

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

(3) PR = 13cm(radius of the quadrant)

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 cm² 

Hence we get the Area of ΔRAS = 30 cm²