In quadrilateral PQRS,PQ = 27 , cm,QR = 30 , | vedclass

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(B) The quadrilateral $PQRS$ is divided into two triangles: $	riangle PQR$ and $	riangle PSR$ by the diagonal $PR = 51 \, cm$.For $	riangle PQR$,th

Vedclass · Accepted Answer

$1494$

Vedclass · Answer

(B) The quadrilateral $PQRS$ is divided into two triangles: $	riangle PQR$ and $	riangle PSR$ by the diagonal $PR = 51 \, cm$.For $	riangle PQR$,the sides are $a = 27 \, cm$,$b = 30 \, cm$,$c = 51 \, cm$.The semi-perimeter $s_1 = (27 + 30 + 51) / 2 = 108 / 2 = 54 \, cm$.Area of $	riangle PQR = \sqrt{s_1(s_1-a)(s_1-b)(s_1-c)} = \sqrt{54(54-27)(54-30)(54-51)} = \sqrt{54 	imes 27 	imes 24 	imes 3} = \sqrt{104976} = 324 \, cm^2$.For $	riangle PSR$,the sides are $a = 52 \, cm$,$b = 53 \, cm$,$c = 51 \, cm$.The semi-perimeter $s_2 = (52 + 53 + 51) / 2 = 156 / 2 = 78 \, cm$.Area of $	riangle PSR = \sqrt{s_2(s_2-a)(s_2-b)(s_2-c)} = \sqrt{78(78-52)(78-53)(78-51)} = \sqrt{78 	imes 26 	imes 25 	imes 27} = \sqrt{1368900} = 1170 \, cm^2$.Total area of quadrilateral $PQRS = 324 + 1170 = 1494 \, cm^2$.

In quadrilateral $PQRS$,$PQ = 27 \, cm$,$QR = 30 \, cm$,$RS = 52 \, cm$,$SP = 53 \, cm$ and $PR = 51 \, cm$,then find the area of the quadrilateral in $cm^2$.

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