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Question

Prove that area of a trapezium is equal to half the product of the sum of parallel sides and distance between the parallel sides.

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Solution

Consider the trapezium ABCD with with AB||CD
AP=BQ=h(say) [distance between parallel lines one equal]
ar(ABCD)=ar(ADC)+ar(ABC).....(1)
ar(ADC)=12×base×height=12×(DC)×h......(2)
ar(ABC)=12×base×height=12×(AB)×h.....(3)
From (1),(2)and (3)
ar(ABCD)=12×h(CD)+12×h(AB)
ar(ABCD)=12h[AB+CD]
Area of a trapezium is half the product of the sum of parallel sides and distance between the parallel sides.

1078872_1122582_ans_d01976d1d060490284245a1fcb44ea69.png

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