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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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 $cm^2$.

Similar Questions

$PQRS$ is a square. If $PR = 10 \, cm$,then the area of $PQRS = \dots \, cm^2$.

Write True or False and justify your answer.
The area of a triangle with base $4 \, \text{cm}$ and height $6 \, \text{cm}$ is $24 \, \text{cm}^2$.

The perimeter of a rhombus is $100\,cm$ and one of its diagonals measures $48\,cm$. Then,the length of the other diagonal is ....... $cm.$

In a kite-shaped quadrilateral $ABCD$,$AB = AD = 12 \, cm$,$CB = CD = 17 \, cm$,and $AC = 25 \, cm$. Find its area and the length of diagonal $BD$.

$A$ rhombus-shaped sheet with a perimeter of $40 \, cm$ and one diagonal of $12 \, cm$ is painted on both sides at the rate of $Rs \, 5$ per $cm^2$. Find the cost of painting (in $Rs$).

Vedclass Test Series

Exam Paper Generator

Online Exam Module