The area A of a rectangle is given by the formula

A = L × W

where L and W are the length and width, respectively, of the of the rectangle.

Example 1

Find the area of a rectangle of length 35 meters and width 20 meters.

Solution to Example 1

Since the length L and the width W have the same units, we apply the formula given above substituting L and W by their values as follows

A = L × W = 35 × 20 = 700 square meters (or m^{ 2})

Example 2

A rectangle field has a length of 360 inches and a width of 300 inches. Find the area of the rectangle in square feet. (1 foot = 12 inches)

Solution to Example 2

Since we need to find the area in square feet, we need to convert the length L and width W in feet.

L = 360 inches = 360 / 12 = 30 feet

W = 300 inches = 300 / 12 = 25 feet

The area A of the rectangle is given by

A = L × W = 30 × 25 = 750 square feet (or ft^{ 2})

Example 3

The width of a rectangle is 20 meters and its length is five fourths of its width. Find the area of this rectangle.

Solution to Example 3

We first need to find length L of the rectangle given its width W = 20 meters.

L = (5/4) × W = (5/4) × 20 = 5 × 20 / 4 = 25 meters

The area A of the rectangle is given by

A = L × W = 25 × 20 = 500 square meters (m^{ 2})

Example 4

The length of a rectangle is 1200 meters and its width is 100 meters shorter that its length. Find the area of this rectangle in square kilometers. (1 kilometer = 1000 meters)

Solution to Example 4

We first need to find the width W of the rectangle given its length L = 1200 meters.

W = 1200 - 100 = 1100 meters

We convert the length L and the width W in kilometers

L = 1200 meters / 1000 = 1.2 kilometers

W = 1100 meters / 1000 = 1.1 kilometers

The area A of the rectangle is calculated as follows

A = L × W = 1.2 × 1.1 = 1.32 square kilometers (or km^{ 2})

Example 5

A rectangular room of length 5 meters and width 4.5 meters is to be tiled with square tiles of 20 cm per side. What is the minimum number of tiles needed?

Solution to Example 5

We need to find the area A1 of one tile in square centimeters.

A1 = 20 × 20 = 400 square centimeters.

We now convert the length L and width W of the room in centimeters and find its area A.

L = 5 × 100 = 500 centimeters

W = 4.5 × 100 = 450 centimeters

A = 500 × 450 = 225,000 square centimeters

The number N of tiles needed is given by dividing the total area of the room by the area of one tile

N = Total area of the room / area of one tile = 225,000 / 400 = 562.5 tiles

The number of tiles must be an integer and also in tiling the room, one might have to cut tiles at some places and therefore more tiles may be needed. Therefore the minimum number of tiles needed is 563.

Length and Width of Rectangle - Geometry Calculator.