Question

A playground is of the shape of a pentagon PQRST as shown in the given figure. Ravi marked the ground in which QM is perpendicular to PR, SN is perpendicular to PR, TO is perpendicular to PR such that PR = 24m, PN = 18m, PO = 10m, QM = 5m, SN = 9m, TO = 7m. Find the area of the playground.​

Answer 1

Step-by-step explanation:

please mark me as brainlist pls help me very urgent and follow

Answer 2

Area

Given:

PQRST is a pentagon, QM is perpendicular to PR

SN is perpendicular to PR, TO is perpendicular to PR

PR = 24m, PN = 18m, PO = 10m, QM = 5m, SN = 9m, TO = 7m

To find:

Area of playground

Explanation:

The figure accomplishing all the conditions in the question is attached.

$Area \ of \ pentagon \ park \ PQRST=ar.(\triangle POT)+ ar.(\triangle SNR)+ ar.(\triangle PQR)+ ar.(quad \ SNOT)$

$ar(\triangle POT)=\frac{1}{2}\times PO\times TO\\\\=\frac{1}{2} \times10\times7=35m^2\\\\ar(\triangle SNR)=\frac{1}{2}\times SN\times NR\\\\\frac{1}{2} \times9\times(24-18)=27m^2\\\\ar(\triangle PQR)=\frac{1}{2}\times PR\times QM\\\\\frac{1}{2} \times24\times5=60m^2\\\\ar(quad \ SNOT)= \frac{1}{2}\times(TO+SN)\times ON \\\\=\frac{1}{2}\times(7+9)\times(18-10)=64 m ^2$

Hence , total area of playground will be $(35+27+60+64)=186 m^2$.

So, the required answer is $186m^2$.