# A triangle has sides with lengths: 14, 9, and 7. How do you find the area of the triangle using Heron's formula?

Dec 30, 2015

The area A is $12 \cdot \sqrt{5}$

#### Explanation:

Heron's formula: A=sqrt(s(s-a)(s-b)(s-c), where s, semiperimeter, is $\frac{a + b + c}{2}$

Applying the formula:
$s = \frac{14 + 9 + 7}{2} = \frac{30}{2} = 15$
$A = \sqrt{15 \cdot \left(15 - 14\right) \left(15 - 9\right) \left(15 - 7\right)}$
$A = \sqrt{15 \cdot 1 \cdot 6 \cdot 8} = \sqrt{720} = 12 \cdot \sqrt{5}$