Question

The equal sides of the isosceles triangle are 12 cm, and the perimeter is 30 cm, then find its area.

Answer 1

Given,
Perimeter = 30cm
Semi perimeter, $s=\frac{30}{2}=15cm$
$a=b=12cm,c=?$
$a+b+c=30$
$12+12+c=30$
$c=30-24=6cm$
By putting the values of s, a, b and c in Heron’s formula, we can get
$A=\sqrt{s(s-a)(s-b)(s-c)}$

$A=\sqrt{15(15-12)(15-12)(15-6)}$

$A=\sqrt{15\times 3\times 3\times 9}$

$=\sqrt{15\times 3\times 3\times 3\times 3}$

$=9\sqrt{15}$Sq. cm