# A triangle has sides with lengths: 7, 9, and 15. How do you find the area of the triangle using Heron's formula?

Jun 13, 2018

$A = \frac{1}{4} \cdot \sqrt{6851}$

#### Explanation:

$p = \frac{7 + 9 + 15}{2} = 15.5$

$A = \sqrt{p \left(p - 7\right) \left(p - 9\right) \left(p - 15\right)}$

$A = \sqrt{15.5 \times 8.5 \times 6.5 \times 0.5}$

$A = \sqrt{\frac{4281875}{10000}} = \sqrt{\frac{13 \cdot 17 \cdot 31}{16}}$