MHB What is the area of an isosceles triangle with side lengths 6, 6, and 4?

[Elissa89]

Side lengths are a=6, b=6, c=4. Find the area

A=1/2*b*h

I split the triangle in half to find the height. Since the base is 4, that divided the base into 2:

2^2+h^2=6^2

4+h^2=36

h^2=32

h=4*sqrt(2)
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1/2*4*4*sqrt(2)=area of 8*sqrt(2)

Did I do this correctly? I do not have an answer key to the study guide I was given.

 

[MarkFL]

Let's check your answer using Heron's formula...the semi-perimeter \(s\) is 8, hence:

$$A=\sqrt{8(8-6)(8-6)(8-4)}=\sqrt{2^7}=8\sqrt{2}\quad\checkmark$$