The image above is a square pyramid frustum.

To compute the volume of a square pyramid frustum, three essential parameters are needed and this parameters are **base side length (a), top side length (b) **and **height (h)****.**

The formula for calculating the volume of a square pyramid frustum:

V = ^{h(a² + ab + b²)} ⁄ _{3}

Where;

V = Volume of a square pyramid frustum

a = Base side length of the square pyramid frustum

b = Top side length of the square pyramid frustum

h = Height of the square pyramid frustum

Let’s solve an example

Find the volume of a square pyramid frustum when the base side length is 10 cm with a top side length of 12 cm and a height of 20 cm.

This implies that;

a = Base side length of the square pyramid frustum = 10 cm

b = Top side length of the square pyramid frustum = 12 cm

h = Height of the square pyramid frustum = 20 cm

V = ^{h(a² + ab + b²)} ⁄ _{3}

V = ^{20(10² + (10 x 12) + 12²)} ⁄ _{3}

V = ^{20(100 + (120) + 144)} ⁄ _{3}

V = ^{20(364)} ⁄ _{3}

V = ^{7280} ⁄ _{3}

V = 2426.6

Therefore, the** volume of the square pyramid frustum** is **2426.6 cm ^{3}.**

**Calculating the Height of a Square Pyramid Frustum when the Volume, Top Side Length and Base Side Length of the Square Pyramid Frustum is Given.**

h = ^{3V} / _{(a2 + ab + b2)}

Where;

h = Height of the square pyramid frustum

V = Volume of the square pyramid frustum

a = Base side length of the square pyramid frustum

b = Top side length of the square pyramid frustum

Let’s solve an example;

Find the height of a square pyramid frustum when the volume is 32 cm^{3}, base side length is 14 cm and top side length is 18 cm.

This implies that;

V = Volume of the square pyramid frustum = 32 cm^{3}

a = Base side length of the square pyramid frustum = 14 cm

b = Top side length of the square pyramid frustum = 18 cm

h = ^{3V} / _{(a2 + ab + b2)}

h = ^{32 x 3} / _{(142 + (14 x 18) + 182)}

h = ^{96} / _{(196 + 252 + 324)}

h = ^{96} / _{772}

h = 0.124

Therefore, the **height of the square pyramid frustum** is **0.124 cm.**