# 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 $\triangle \mathrm{PQR}$.

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 $96\ cm^2$.

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Updated on: 10-Oct-2022

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