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.

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