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PQRS is a trapezium having PS and QR as parallel sides. A is any point on PQ and B is a point on SR such that AB || QR. If area of ΔPBQ is 17cm2, find the area of ΔASR. - Mathematics

Answer in Brief

PQRS is a trapezium having PS and QR as parallel sides. A is any point on PQ and is a point on SR such that AB || QR. If area of ΔPBQ is 17cm2, find the area of ΔASR.

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Solution

Given: Here from the given figure we get

(1) PQRS is a trapezium having PS||QR

(2) A is any point on PQ

(3) B is any point on SR

(4) AB||QR

(5) Area of ΔBPQ = 17 cm2

 To find : Area of ΔASR

Calculation: We know that ‘If a triangle and a parallelogram are on the same base and the same parallels, the area of the triangle is equal to half the area of the parallelogram’

Here we can see that:

Area (ΔAPB) = Area (ΔABS) …… (1)

And, Area (ΔAQR) = Area (ΔABR) …… (2)

Therefore,

Area (ΔASR) = Area (ΔABS) + Area (ΔABR)

From equation (1) and (2), we have,

Area (ΔASR) = Area (ΔAPB) + Area (ΔAQR)

⇒ Area (ΔASR) = Area (ΔBPQ) = 17 cm2

Hence, the area of the triangle ΔASR is 17 cm2.

 

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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 14 Areas of Parallelograms and Triangles
Q 8 | Page 60
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