How do you use Heron's formula to find the area of a triangle with sides of lengths 14 , 8 , and 15 ?

1 Answer
Jan 21, 2016

Area=55.31218 square units

Explanation:

Hero's formula for finding area of the triangle is given by
Area=sqrt(s(s-a)(s-b)(s-c))

Where s is the semi perimeter and is defined as
s=(a+b+c)/2

and a, b, c are the lengths of the three sides of the triangle.

Here let a=14, b=8 and c=15

implies s=(14+8+15)/2=37/2=18.5

implies s=18.5

implies s-a=18.5-14=4.5, s-b=18.5-8=10.5 and s-c=18.5-15=3.5

implies s-a=4.5, s-b=10.5 and s-c=3.5

implies Area=sqrt(18.5*4.5*10.5*3.5)=sqrt3059.4375=55.31218 square units

implies Area=55.31218 square units