Areas of Squares and Rectangles

The simplest (and most commonly used) area calculations are for squares and rectangles.

To find the area of a rectangle multiply its height by its width.

For a square you only need to find the length of one of the sides (as each side is the same length) and then multiply this by itself to find the area. This is the same as saying length2 or length squared.

It is good practice to check that a shape is actually a square by measuring both sides.
For example your lawn may look same length on both side or square however when you measure it each side is different. Alway use the largest of the 2 numbers so you don’t short change yourself on materials.

Box 1 = 20ft x 10ft = 200 square feet

Box 2 = 10ft x 10ft = 100 square feet

A typical backyard is often more complex than a simple rectangle or square. The following diagrams will help you breakdown your measurements by section.

To determine the square feet of this shape you can divide the area into two squares, then simply add the two areas together.

Area 1 = 18ft x 17ft= Total 306 sq.ft.

Area 2 = 10ft x 8ft =Total 80 sq.ft.

Total area of Area 1 + 2: 306+80 = 386 sq.ft.

How to calculate areas of circles

The diameter of a circle is the length of a straight line from one side of the circle to the other that passes through the central point of the circle. The diameter is twice the length of the radius (diameter = radius × 2)

The radius of a circle is the length of a straight line from the central point of the circle to its edge. The radius is half of the diameter. (radius = diameter ÷ 2)

You can measure the diameter or radius at any point around the circle – the important thing is to measure using a straight line that passes through (diameter) or ends at (radius) the centre of the circle.

When measuring circles it’s easier to measure the diameter, then divide by 2 to find the radius.

The radius is needed to work our the area of a circle.The formula is:

circle area = πR2.

This means:

π = Pi is a constant that equals 3.142.

R = is the radius of the circle.

R2 (radius squared) means radius × radius.

Therefore a circle with a radius of 7 ft, has an area of:

3.142 × 9 × 9 = 153.958 square feet or 154 sq.ft.

A circle with a diameter of 18 ft has an area:

First we work out the radius (18ft ÷ 2 = 9 ft )

Then apply the formula:

3.142 × 9 x 9 = 254.502 square feet

The area of a circle with a diameter of 18 feet is 254.5 sq.ft.

CAUTION: Your circle square feet is not what you need to purchase artificial turf. Ask us for
help to determine your actual requirements.

Areas of Borders

This example shows a path around a field – the path is 6 feet wide.

Again, there are several ways to work out the area of the path in this example.

You could view the path as four separate rectangles, calculate their dimensions and then their area and finally add the areas together to give a total.

A faster way would be to work out the area of the whole shape and the area of the internal rectangle. Subtract the internal rectangle area from the whole, leaving the area of the path.

Calculation of the Border would be as follows:

First determine the whole area: 25ft x 12ft = 300 square feet

Second subtract the borders sides from the length and width:

Width 12 ft – 3ft – 3 ft = 6

Length 25 – 3 ft – 3 ft = 19

Third determine the middle section area is 6ft x 19 ft = 114 sq,ft,

Finally calculate the border area:  whole area minus middle area: 300 – 114 = 186 sq.ft.

Areas of Triangles

Assuming you know (or can measure) the dimensions of a triangle then you can quickly work out its area.

The area of a triangle is (height × width) ÷ 2.

In other words you can work out the area of a triangle in the same way as the area for a square or parallelogram just divide your answer by 2.

The height of a triangle is measured as a right-angled line from the bottom line to the ‘apex’ (top point) of the triangle.


Square feet needed for Triangle 1 and Triangle 2 are the same:

16 ft x 20ft = 320 divided by 2 = 160 square feet

Square feet for triangle 3 is 14 ft x 20 ft = 280 divided by 2 = 140 square feet

CAUTION: Your triangle square feet is not what you need to purchase artificial turf. Ask us for help to determine your actual requirements.

Volume Formula

To determine how much fill your may need you much know how to determine the volume of

Square or Rectangle =

Length x width x height

If you need 4 inches of fill that is your height.  However you need to convert 4 inches in feet, which is .3 of a foot(12divided by 4=3)

10 ft x 8 ft x .3 ft = 24 cubic feet

Circle or sphere =

  • Find the radius of the circle
  • Calculate the area of the circle
  • Find the height of the cylinder.
  • Multiply the area of the base by the height.

4 inches of fill must be converted to feet = .3 feet

Area = 3.142 x 4 x 4 = 50.272

Volume = 50.272 x .3 = 15 cubic

your area.  Here is how to calculate it.