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Constructions

Question

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

Solution

Given: ABCD is a trapezium with AB || CD. AM is its height.

To Prove: ar(trapezium ABCD)

equals 1 half left parenthesis AB plus DC right parenthesis left parenthesis AM right parenthesis

Construction: Join AC Proof: ar(trapezium ABCD)

equals space ar space left parenthesis increment ADC right parenthesis plus ar left parenthesis increment ABC right parenthesis equals space 1 half cross times DC cross times AM plus 1 half cross times AB cross times AM equals space 1 half cross times left parenthesis DC plus AB right parenthesis cross times AM equals space 1 half open parentheses AB plus DC close parentheses left parenthesis AM right parenthesis

Some More Questions From Constructions Chapter

Prove that of all parallelograms of which the sides are given, the parallelogram which is a rectangle, has the greatest area.

In the figure, diagonals AC and BD of a trapezium ABCD with AB || CD intersect each other at O. Show that ar(Δ AOD) = ar(Δ BOC).

Parallelograms on the same base and between same parallels are equal in area. Prove this.

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