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Altitude of a Pyramid

Altitude of a Pyramid is defined as the perpendicular distance from the vertex to the base of the pyramid. It is also called as the height of the pyramid.

Pyramid is a type of three dimensional shapes. The name of the pyramid will be varied depending upon the shape of the base. For example, if the base of the pyramid is hexagon, the pyramid is called as hexagonal pyramid. In this tutorial, we shall see how to find the altitude of the pyramid.

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Altitude of a Pyramid Formula

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Altitude of a Square pyramid:

Altitude of a Pyramid

Volume of a regular square pyramid (v) = `1/3` a2 h cubic units

a – side length

h – (Altitude) height

Altitude of the square pyramid (h) = `(3V) / (a^2)` units

Altitude of a Pentagonal Pyramid

Altitude of a Pyramid Formula

Volume of regular pentagonal pyramid (v) = `1/3` x 1.72 a2 x h cubic unit

a – side length

h – Height

Altitude of the pentagonal pyramid (h) = `(3V) / (1.72a^2)` units

Altitude of a Pyramid Solved Examples

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Given below are some of the examples to find the altitude of a pyramid

Example1:

The square pyramid has the volume = 141.17 cm3 and side length = 5.5 cm. Find the altitude of the pyramid.

Solution:

Given:

Volume of the square pyramid (V) = 141.17 cm3

Side length (a) = 5.5 cm

Formula:

Altitude of the square pyramid (h) = `(3V) / (a^2)` units

= `(3 X 141.17) / (5.5^2)`

= `423.51 / 30.25`

= 14

Altitude of the square pyramid (h) = 14 cm

Example 2:

The square pyramid has the volume = 225.33 cm3 and side length = 6.5 cm. Find the altitude of the pyramid.

Solution:

Given:

Volume of the square pyramid (V) = 225.33 cm3

Side length (a) = 6.5 cm

Formula:

Altitude of the square pyramid (h) = `(3V) / (a^2)` units

= `(3 X 225.33) / (6.5^2)`

= `675.99 / 42.25`

= 16

Altitude of the square pyramid (h) = 16 cm

Example 3:

The pentagonal pyramid has the volume = 192 cm3 and side length = 6 cm. Find the altitude of the pyramid.

Solution:

Given:

Volume of the pentagonal pyramid (V) = 192 cm3

Side length (a) = 6 cm

Formula:

Altitude of the pentagonal pyramid (h) = `(3V) / (1.72a^2)` units

= `(3 X 192) / (1.72 X 6^2)`

= `576 / 61.92`

= 9.3

Altitude of the pentagonal pyramid (h) = 9.3 cm

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