# How do you use Heron's formula to find the area of a triangle with sides of lengths 12 , 5 , and 9 ?

Area $= 4 \sqrt{26} \text{ }$square units

#### Explanation:

Given sides
Let $a = 12$ and $b = 5$ and $c = 9$

solve half of perimeter $s$ first

$s = \frac{a + b + c}{2} = \frac{12 + 5 + 9}{2} = 13$

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

Area $= \sqrt{13 \left(13 - 12\right) \left(13 - 5\right) \left(13 - 9\right)}$

Area $= 4 \sqrt{26} \text{ }$square units

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