How do you use Heron's formula to find the area of a triangle with sides of lengths #23 #, #21 #, and #20 #?

1 Answer
Anthony X
Feb 10, 2016

Find the semiperimeter first then use Heron's formula
Area is #24sqrt(66)#

Explanation:

Heron's formula states that
Area = #sqrt(s(s-a)(s-b)(s-c))#

Where s is the sum of all sides / 2 (Also known as the semiperimeter)
a,b,c are the side lengths

From here, you can just plug in all the values.
Find that s = 32
Area = #sqrt(32(9)(11)(12))#
prime factorize the inside to get #sqrt((2^7)(3^3)(11))#

Then take out the squares to get
#2^3 * 3##sqrt(2*3*11)#
Finally
#24sqrt(66)#

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