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Question
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.
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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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