PQRS is a rectangle inscribed in a quadrant of a circle of radius 13 c

1.	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» Given that, PQRS is a rectangle PS = 5 cm PR = 13 cm In triangle PSR, by using Pythagoras theorem SR² = PR²– PS² SR² = (13)² – (5)² SR² = 169 – 25 SR² = 114 SR = 12 cm We have to find the area ΔRAS, Area (ΔRAS) = \(\frac{1}{2}\) x Base x Height = \(\frac{1}{2}\) x SR x PS = \(\frac{1}{2}\) x 12 x 5 = 30 cm² Hence, Area (ΔRAS) is 30 cm²

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»

Given that,

PQRS is a rectangle

PS = 5 cm

PR = 13 cm

In triangle PSR,

by using Pythagoras theorem

SR² = PR²– PS²

SR² = (13)² – (5)²

SR² = 169 – 25

SR² = 114

SR = 12 cm

We have to find the area ΔRAS,

Area (ΔRAS) = \(\frac{1}{2}\) x Base x Height

= \(\frac{1}{2}\) x SR x PS

= \(\frac{1}{2}\) x 12 x 5

= 30 cm²

Hence,

Area (ΔRAS) is 30 cm²