In parallelogram ABCD,AB = 9 , cm,BC = 10 , c | vedclass

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Question

(D) In parallelogram $ABCD$,the diagonal $AC$ divides the parallelogram into two congruent triangles,$	riangle ABC$ and $	riangle ADC$.We calculate

Vedclass · Accepted Answer

$72$

Vedclass · Answer

(D) In parallelogram $ABCD$,the diagonal $AC$ divides the parallelogram into two congruent triangles,$	riangle ABC$ and $	riangle ADC$.We calculate the area of $	riangle ABC$ using Heron's formula.The sides of $	riangle ABC$ are $a = 9 \, cm$,$b = 10 \, cm$,and $c = 17 \, cm$.The semi-perimeter $s = (a + b + c) / 2 = (9 + 10 + 17) / 2 = 36 / 2 = 18 \, cm$.Area of $	riangle ABC = \sqrt{s(s-a)(s-b)(s-c)} = \sqrt{18(18-9)(18-10)(18-17)} = \sqrt{18 	imes 9 	imes 8 	imes 1} = \sqrt{1296} = 36 \, cm^2$.Since the area of the parallelogram is twice the area of $	riangle ABC$,the total area $= 2 	imes 36 = 72 \, cm^2$.

In parallelogram $ABCD$,$AB = 9 \, cm$,$BC = 10 \, cm$ and $AC = 17 \, cm$,then find its area. (in $, cm^2$)

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