# What is the formula for calculating the length of the diagonal of a right rectangular prism?

The diagonal of a right rectangular prism is the line that connects opposite vertices of a prism.

## Answer: The formula for calculating the length of the diagonal of a right rectangular prism is √(l^{2}+w^{2}+h^{2}). where l is the length, w is the width and h is the height.

To find the formula of diagonal of a right rectangular prism, we must have the length, width, and height of a prism.

**Explanation:**

Look at the figure of a right rectangular prism shown below.

The formula for the length of the diagonal of a right rectangular prism is: d = √(l^{2}+w^{2}+h^{2})

Here, d = length of the diagonal, l = length of the rectangular base of the prism, w = width of the rectangular base of the prism, and h = height of the prism.

Let us find the diagonal of a right rectangular prism with a length of 20 units, the width of 10 units, and the height of 5 units.

The formula for the length of the diagonal of a right rectangular prism = √(l^{2 }+ w^{2 }+ h^{2}) units.

Substitute the value in the formula,

= √(20^{2 }+ 10^{2 }+ 5^{2}) units

= 22.91 units

### So, the formula for the length of the diagonal of a right rectangular prism is √(l^{2}+w^{2}+h^{2}), where l is the length, b is the breadth and h is the height of a right rectangular prism.

visual curriculum