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

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?

150150150120120120150150150

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
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

Step-by-step written solution

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1

Understand the problem

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?

150150150120120120150150150

2

Step-by-step solution

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

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

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

X2+H2=1502 X^2+H^2=150^2

We insert the corresponding data:

602+h2=1502 60^2+h^2=150^2

Finally we extract the root: h=1502−602=22500−3600=18900 h=\sqrt{150^2-60^2}=\sqrt{22500-3600}=\sqrt{18900}

h=3021 h=30\sqrt{21}

3

Final Answer

3021 30\sqrt{21} m

Practice Quiz

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Consider a right-angled triangle, AB = 8 cm and AC = 6 cm.
Calculate the length of side BC.

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