# In $\triangle \mathrm{ABC}, \mathrm{M}$ and $\mathrm{N}$ are the midpoints of $\mathrm{AB}$ and $\mathrm{AC}$ respectively. If the area of $\triangle \mathrm{ABC}$ is $90 \mathrm{~cm}^{2}$, find the area of $\triangle \mathrm{AMN}$.

Given:

In $\triangle \mathrm{ABC}, \mathrm{M}$ and $\mathrm{N}$ are the midpoints of $\mathrm{AB}$ and $\mathrm{AC}$ respectively.

The area of $\triangle \mathrm{ABC}$ is $90 \mathrm{~cm}^{2}$.

To do:

We have to find the area of $\triangle \mathrm{AMN}$.

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 AMN $=\frac{1}{4}\times$ Area of triangle ABC

Area of triangle AMN $=\frac{1}{4}\times 90\ cm^2$

Area of triangle AMN $=22.5\ cm^2$

The area of $\triangle \mathrm{AMN}$ is $22.5\ cm^2$.

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Updated on: 10-Oct-2022

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