Question:
Find the area of an isosceles triangle each of whose equal sides measures 13 cm and whose base measures 20 cm.
Solution:
We have :
$a=13 \mathrm{~cm}$ and $b=20 \mathrm{~cm}$
$\therefore$ Area of isosceles triangle $=\frac{b}{4} \sqrt{4 a^{2}-b^{2}}$
$=\frac{20}{4} \times \sqrt{4(13)^{2}-20^{2}}$
$=5 \times \sqrt{676-400}$
$=5 \times \sqrt{276}$
$=5 \times 16.6$
$=83.06 \mathrm{~cm}^{2}$