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 $22.5\ cm^2$.

Tutorialspoint
Tutorialspoint

Simply Easy Learning

Updated on: 10-Oct-2022

38 Views

Kickstart Your Career

Get certified by completing the course

Get Started
Advertisements