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 ar(ΔPAS) = _______.

Answer 1

Given:
PQRS is a rectangle inscribed in a quadrant of a circle of radius 13 cm
PS = 5 cm
A is any point on PQ


QS = radius of the circle = 13 cm ...(1)

In ΔPQS
Using pythagoras theorem,
QS² = PS² + PQ²
⇒ 13² = 5² + PQ²
⇒ PQ² = 169 − 25
⇒ PQ² = 144
⇒ PQ = 12 cm = SR ...(2)


Thus,
ar(ΔRAS) = $\frac{1}{2}$× base × height
= $\frac{1}{2}$× SR × PS
= $\frac{1}{2}$× 12 × 5
= 30 cm²


Hence, ​ar(ΔRAS) = 30 cm².

Disclaimer: The question is to find the area of ΔRAS instead of the area of ΔPAS.