# A triangle has sides with lengths: 14, 15, and 7. How do you find the area of the triangle using Heron's formula?

Apr 2, 2016

$2 \sqrt{594}$

#### Explanation:

Use Heron's formula

color(blue)(area=sqrt(s(s-a)(s-b)(s-c))

Where

color(orange)((a,bandc)=sides,s=(a+b+c)/2

So,

color(purple)(a=14,b=15,c=7,s=(14+15+7)/(2)=36/2=18

$\therefore a r e a = \sqrt{18 \left(18 - 14\right) \left(18 - 15\right) \left(18 - 7\right)}$

$\rightarrow \sqrt{18 \left(4\right) \left(3\right) \left(11\right)}$

$\rightarrow \sqrt{18 \left(132\right)}$

$\rightarrow \sqrt{2376}$

$\rightarrow \sqrt{4 \cdot 594}$

color(green)(rArr2sqrt594~~48.7bar5