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 17 cm², find the area of ΔASR.
Answers
Given : 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 and area of ΔPBQ is 17 cm².
To find : Area of ΔASR.
Proof :
We have , PQRS a trapezium and PS ‖ QR and AB ‖ QR.
We know that, triangles on the same base and between the same parallels are equal in area.
Here,
ar (∆ABP) = ar (∆ASB) ………... (1)
ar (∆ARQ) = ar (∆ARB) …………. (2)
Now,
ar (∆ASR) = ar (∆ASB) + ar (∆ARB)
ar (∆ASR) = ar (∆ABP + ar (∆ARQ)
[From eq 1& 2]
ar (∆ASR) = ar (∆PBQ)
ar (∆ASR) = 17 cm² [Given : ar (∆PBQ) = 17 cm²]
Hence, the Area (∆ASR) is 17 cm².
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Here,
ar (∆ABP) = ar (∆ASB) ………... (1)
ar (∆ARQ) = ar (∆ARB) …………. (2)
Now,
ar (∆ASR) = ar (∆ASB) + ar (∆ARB)
ar (∆ASR) = ar (∆ABP + ar (∆ARQ)
[From eq 1& 2]
ar (∆ASR) = ar (∆PBQ)
ar (∆ASR) = 17 cm² [Given : ar (∆PBQ) = 17 cm²]