# How do you use Heron's formula to determine the area of a triangle with sides of that are 35, 28, and 21 units in length?

Jan 16, 2016

$294$ ${\text{units}}^{2}$

#### Explanation:

First, determine the semiperimeter $s$ of the triangle (which has sides $a , b , c$).

$s = \frac{a + b + c}{2}$

We know that $a = 35 , b = 28 , c = 21$ so

$s = \frac{35 + 28 + 21}{2} = 42$

Plug these into Heron's formula, which determines the area of a triangle:

$A = \sqrt{s \left(s - a\right) \left(s - b\right) \left(s - c\right)}$

$A = \sqrt{42 \left(42 - 35\right) \left(42 - 28\right) \left(42 - 21\right)}$

$A = \sqrt{42 \times 7 \times 14 \times 21}$

$A = \sqrt{{2}^{2} \times {3}^{2} \times {7}^{4}}$

$A = 2 \times 3 \times {7}^{2}$

$A = 294$