# How do you use Heron's formula to find the area of a triangle with sides of lengths 15 , 16 , and 14 ?

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1s2s2p Share
Mar 8, 2018

$\text{Area} \approx 96.56$

#### Explanation:

Heron's formula says that:
$\text{Area} = \sqrt{S \left(S - A\right) \left(S - B\right) \left(S - C\right)}$ given $S = \frac{A + B + C}{2}$

For this triangle, $S = \frac{14 + 15 + 16}{2} = 22.5$

$\text{Area} = \sqrt{22.5 \left(22.25 - 14\right) \left(22.5 - 15\right) \left(22.5 - 16\right)} = \sqrt{\frac{149175}{16}} = \frac{15 \sqrt{663}}{4} \approx 96.56$

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