# Diagonal of a Rectangle

LAST UPDATE: February 2nd, 2022

## Method #1 – Diagonal from Length & Width

### Formula – How to calculate the area of a rectangle from the length & width

Diagonal = √(Length2 + Width2)

##### Example

A rectangle has a length of 10 and a width of 30.

Diagonal = √(102 + 302) = √(100 + 900) = √1000 = 31.62

## Method #2 – Diagonal from Area

### Formula – How to calculate the diagonal of a rectangle using the area

Step 1: Find the Width

Width = Area / Length

Step 2: Find the diagonal

Diagonal = √(Length2 + Width2)

##### Example

A rectangle has a length of 10 and an area of 200.

Width = 200 / 100 = 20

Diagonal = √(102 + 202) = √(100 + 400) = √500 = 22.36

## Method #3 – Diagonal from Perimeter

### Formula – How to calculate the diagonal of a rectangle using the perimeter

Step 1: Find the Width

Width = (Perimeter – Length x 2) ÷ 2

Step 2: Find the diagonal

Diagonal = √(Length2 + Width2)

##### Example

A rectangle has a length of 10 and a perimeter of 90.

Width = (90 – 10 x 2) ÷ 2 = (90 – 20) ÷ 2 = 70 ÷ 2 = 35

Diagonal = √(102 + 352) = √(100 + 1225) = √1325 = 36.40