A triangle has sides with lengths: 7, 6, and 8. How do you find the area of the triangle using Heron's formula?

1 Answer
Roella W.
Dec 21, 2015

Substitute the lengths into the formula and calculate.

Explanation:

Heron's formula states that the area of a triangle whose sides have lengths a, b, and c is
A={\sqrt {s(s-a)(s-b)(s-c)}}
where s is the semiperimeter of the triangle; that is,
s={\frac {a+b+c}{2}}
In this example s = (7 + 6 + 8)/2 = 21/2
s - a = 21/2 - 7 = (21- 7*2)/2 = 7/2
s - b = 21/2 - 6 = (21 - 12)/2 - 9/2
s - c = 21/2 - 8 = 5/2
A = sqrt(21/2 * 7/2 * 9/2 * 5/2)
A = sqrt((21*7*9*5)/16)
A= sqrt(3*7*7*3*3*5)/4
A=7*3*sqrt(3*5)/4
A=21*sqrt(15)/4

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