# What is the area of a triangle with sides 10, 10 and 16?

Jun 1, 2015

The height of a triangle with sides 10, 10, and 16, if we use 16 as the base is 6 (Pythagorean Theorem and diagram below).

Therefore the area of the triangle is
$A = \frac{1}{2} b h = \frac{1}{2} \cdot 16 \cdot 6 = 48$

Alternately you could use Heron's formula
$A = \sqrt{s \left(s - a\right) \left(s - b\right) \left(s - c\right)}$ for a triangle with sides $a , b , \mathmr{and} c$ and a semi-perimeter of $s$.

In this case $s = 18$
and
the area $= \sqrt{18 \left(8\right) \left(8\right) \left(2\right)} = \sqrt{36 \cdot {8}^{2}} = 6 \cdot 8 = 48$