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E is the mid-point of the non-parallel side BC of a trapezium ABCDjoined to the opposite vertices A and D. Prove thatar (AABE) + ar (ADCE)ar (trapezium ABCD) |
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Answer» given : ABCD is a trapezium . such that AB || DC.E is the mid-point of BC.TPT:area(∆ABE)+area(∆DEC)=1/2*area(trapeziumABCD)proof:area(∆ABE) = 1/2*area(∆ABC) ..........(1) [since the median divides the triangle into equal parts]similarly area(∆DEC) = 1/2*area(∆BDC)...........(2)area(∆BDC)=area(∆ADC) [triangles formed between same pair of parallel lines and with the same base are equal in areas]thereforearea(∆DEC)=1/2*area(∆ADC)......(3)adding eq(1) and eq(3):area(∆ABE)+area(∆DEC)=1/2*[area(∆ABC)+area(∆ADC)]=1/2*area(trapeziumABCD) give figure of this question. |
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