How do we find the height of a triangle given the 3 side lengths? We can handle this problem in many ways. One method involves the use of Heron's formula for the area of a triangle. In today's geometry video lesson, we do just that! We go over how to find the height of a triangle when all we know are its side lengths by using Heron's formula and one other formula we're probably all more familiar with.

We'll go over an example problem, discuss what Heron's formula is and how to use it, including what the semiperimeter of a triangle is and how to find it, it's gonna be great! We also provide two example problems at the end.

SOLUTIONS TO EXAMPLE PROBLEMS:

1) The semiperimeter is 5, so the area, using Heron's formula, is sqrt(20) = sqrt(4*5) = 2*sqrt(5)

Recall the base of the triangle is 3. Thus, the height of the triangle is ( 2*2*sqrt(5) ) / 3 = ( 4*sqrt(5) ) / 3, which is approximately 2.98.

2) The semiperimeter is 19/2 or 9.5, so the area, using Heron's formula, is sqrt(195.9375).

Recall the base of the triangle is 7. Thus, the height of the triangle is ( 2*sqrt(195.9375) ) / 7, which is approximately 4.


I hope you find this video helpful, and be sure to ask any questions down in the comments!

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The outro music is by a favorite musician of mine named Vallow, who, upon my request, kindly gave me permission to use his music in my outros. I usually put my own music in the outros, but I love Vallow's music, and wanted to share it with those of you watching. Please check out all of his wonderful work.

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