An isosceles triangle has perimeter $ 30 \mathrm{~cm} $ and each of the equal sides is $ 12 \mathrm{~cm} $. Find the area of the triangle.

AcademicMathematicsNCERTClass 9

 An isosceles triangle has perimeter $30\ cm$ and each of the equal sides is $12\ cm$.

To do:

Let us assume the third side of the triangle as $x$

We have,

Two sides with equal length of $12\ cm$

and perimeter as $30\ cm$

We know that,

Perimeter $P$ of a triangle with sides of length $a\ units, b\ units$ and $c\ units$ 

$P=(a+b+c)\ units$.

This implies,

$30\ cm=12\ cm+12\ cm+x\ cm$

$30\ cm=24\ cm+x\ cm$

This implies,

$x\ cm=30\ cm-24\ cm$

$x\ cm=6\ cm$

By Heron's formula:






$S=15\ cm$

This implies,



$A=9\sqrt{15}\ cm^2$


The area of the triangle is $9\sqrt{15}\ cm^2$.

Updated on 10-Oct-2022 13:41:58