Calculate Pyramid Height: 150m Sides and 120m Base Using Geometry

Question

The Egyptians decided to build another pyramid that looks like an isosceles triangle when viewed from the side.

Each side of the pyramid measures 150 m, while the base measures 120 m.

What is the height of the pyramid?

00:00 What is the height of the pyramid?

00:03 In an isosceles triangle, the height is also a median

00:06 Let's mark half the side length as X

00:10 Let's substitute the side value according to the given data and solve

00:16 We'll use the Pythagorean theorem to find height H

00:22 Let's substitute the value of X

00:26 Let's isolate height H

00:37 And this is the solution to the question

Since the height divides the base into two equal parts, each part will be called X

We begin by calculating X: $120:2=60$

We then are able to calculate the height of the pyramid using the Pythagorean theorem:

$X^2+H^2=150^2$

We insert the corresponding data:

$60^2+h^2=150^2$

Finally we extract the root: $h=\sqrt{150^2-60^2}=\sqrt{22500-3600}=\sqrt{18900}$

$h=30\sqrt{21}$

$30\sqrt{21}$ m