# A triangle has sides with lengths: 16, 11, and 19. How do you find the area of the triangle using Heron's formula?

##### 1 Answer

Jun 21, 2016

≈ 87.91 square units

#### Explanation:

This is a 2 step process.

Step 1: Calculate half the perimeter (s ) of the triangle.

#color(red)(|bar(ul(color(white)(a/a)color(black)(s=(a+b+c)/2)color(white)(a/a)|)))#

where a , b and c are the 3 sides of the triangle.here let a = 16 , b = 11 and c = 19

#rArrs=(16+11+19)/2=46/2=23#

Step 2: Calculate area (A ) using the following

#color(red)(|bar(ul(color(white)(a/a)color(black)(A=sqrt(s(s-a)(s-b)(s-c)))color(white)(a/a)|)))#

#A=sqrt(23(23-16)(23-11)(23-19))#

#=sqrt(23xx7xx12xx4)≈87.91" square units"#