# How do you use Heron's formula to find the area of a triangle with sides of lengths #2 #, #7 #, and #7 #?

##### 1 Answer

Jan 21, 2016

#### Explanation:

In order to use Heron's formula, we will have to know the semiperimeter of the triangle. The semiperimeter is simply one half the perimeter of the triangle, so the semiperimeter

#s=(a+b+c)/2#

Thus, our current semiperimeter is

#s=(2+7+7)/2=8#

Now, we can apply Heron's formula, which states that the area

#A=sqrt(s(s-a)(s-b)(s-c))#

We know that

#A=sqrt(8(8-2)(8-7)(8-7))#

#A=sqrt48#

#A=4sqrt3#