In $ \Delta \mathrm{PQR}, \mathrm{M} $ and $ \mathrm{N} $ are the midpoints of $ \mathrm{PQ} $ and PR respectively. If the area of $ \triangle \mathrm{PMN} $ is $ 24 \mathrm{~cm}^{2} $, find the area of $ \triangle \mathrm{PQR} $.

Academic Mathematics NCERT Class 10

Given:

In \( \Delta \mathrm{PQR}, \mathrm{M} \) and \( \mathrm{N} \) are the midpoints of \( \mathrm{PQ} \) and PR respectively.

The area of \( \triangle \mathrm{PMN} \) is \( 24 \mathrm{~cm}^{2} \).

To do:

We have to find the area of \( \triangle \mathrm{PQR} \).

Solution:

We know that,

Area of the triangle formed by joining the midpoints of the sides of a triangle is equal to one-fourth the area of the given triangle.

Similarly,

Area of the triangle formed by a vertex and the midpoints of the adjacent sides is equal to one-fourth the area of the given triangle.

Therefore,

Area of triangle PMN $=\frac{1}{4}\times$ Area of triangle PQR

$\Rightarrow 24=\frac{1}{4}\times$ Area of triangle PQR

Area of triangle PQR $=24\times4=96\ cm^2$

The area of \( \triangle \mathrm{PQR} \) is $96\ cm^2$.

Simply Easy Learning

Updated on: 10-Oct-2022

26 Views

Kickstart Your Career

Get certified by completing the course

Advertisements