How do you use Heron's formula to find the area of a triangle with sides of lengths #4 #, #8 #, and #5 #?

1 Answer
Meave60
Feb 12, 2016

#A=8.1815#

Explanation:

Heron's formula is #A=sqrt(s(s-a)(s-b)(s-c)#, where #A# is area, #a, b, and c# are the sides, and #s# is the semiperimeter, which is the perimeter divided by #2#. Side #a=4#, side #b=8#, and side #c=5#.

First determine #s#.
#s=(a+b+c)/2#

#s=(4+8+5)/2#

#s=17/2#

#s=8.5#

Use Heron's formula to find the area of the triangle.

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

Substitute the known values into the equation.

#A=sqrt((8.5)(8.5-4)(8.5-8)(8.5-5)#

Simplify.

#A=sqrt((8.5)(4.5)(0.5)(3.5)#

Simplify.

#A=sqrt(66.9375)#

Take the square root.

#A=8.1815# square units to four decimal places.

Related questions
See all questions in Heron's Formula
Impact of this question
2546 views around the world
You can reuse this answer
Creative Commons License