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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)
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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
(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
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