How to Find the Height of an Isosceles Triangle

Are you stuck on a geometry problem, trying to figure out how to find the height of an isosceles triangle? If so, you're in the right place. In this article, we'll break down the formula for finding the height of an isosceles triangle, step by step.

What is an Isosceles Triangle?

An isosceles triangle is a triangle with two congruent sides. This means that the two sides are the same length. The angles opposite these two sides will also be the same. The third side, called the base, can be any length.

How to Calculate the Height of an Isosceles Triangle

The formula for finding the height of an isosceles triangle is as follows:

Height = (base * √(4p^2 - base^2)) / 2p

Let's break this down. The base is the length of the third side of the triangle. The p is the perimeter of the triangle. To find the perimeter, you simply add up all three sides of the triangle. So, if your triangle has sides of length 4, 4, and 8, your perimeter would be 16. Once you have the base and the perimeter, you can plug the numbers into the formula to calculate the height.

Example Problem

Let's try an example problem. Say you have an isosceles triangle with sides of length 4, 4, and 8. To find the height, we first need to calculate the perimeter. The perimeter is 16 (4 + 4 + 8 = 16). Plugging this into the formula, we get: