How To Calculate Area, Perimeter And Volume

The measurement of area, perimeter, and volume is crucial to construction projects, crafts, and other applications.

Area is the space inside the boundary of a two-dimensional shape. Perimeter is the distance around a two-dimensional shape such as a square or circle. Volume is a measure of the three-dimensional space taken up by an object, such as a cube. If you know the object's dimensions, then measurement of area and volume is easy.

Surface area and volume formulas for all everyday geometric shapes can easily be found online, although it's not a bad idea to review how to derive these on your own should the need arise. You can also often get one of these from another; for example, if you know the formula for the area of a circle, you may be able to figure out that the volume of a cylinder is just the area of the associated circle(s) at the end times the cylinder's height.

Step 1

Record the length (​l​) and width (​w​) of a square or rectangle. Substitute your measurements into the formula

\(A=l\times w\)

to solve for area (​A​). In this example, a rectangular garden measures 5m by 7m.

Calculating the area of the garden, we get:

\(A=5\text{ m}\times7\text{ m} = 35\text{ m}^2\)

The area of the garden is 35 meters squared or 35 square meters.

Step 1

Measure the base (​b​) and height (​h​) of the triangle. Use the formula

\(A=\frac{1}{2}bh\)

to find the area of a triangle. A triangle with a height of 7m and a base of 3m has an area of

\(A=\frac{1}{2}(7\text{ m})(3\text{ m})=10.5\text{ m}^2\)

The area (​A​) of the triangle is 10.5 meters squared or 10.5 square meters.

Step 1

Measure the radius (​r​) of the circle. Multiply π (3.14) by the square of the radius to solve for the area (​A​) of a circle.

\(A=\pi r^2\)

For example, a circle with a radius (​r​) of 5 inches will have an area of

\(A=\pi (5\text{ in})^2=78.5\text{ in}^2\)

The area (​A​) of a circle with a radius of 5 inches is 78.5 square inches.

Step 1

Record the lengths of all sides of the square, rectangle, or triangle.

Step 2

Add the measurements to get the value of the perimeter (​P​). For example, a rectangular garden measures 5m by 7m has two sides measuring 5m and two sides measuring 7m. The perimeter (​P​) is:

\(P = 5 + 5 + 7 + 7 = 24\text{ meters}\)

The perimeter of the rectangular garden is 24 meters.

Step 1

Use the formula

\(P=2\pi r\)

to find the perimeter, or circumference, of a circle. For example, a circle with a radius of 3 inches has a circumference of

\(P=2\pi (3)=18.8\text{ inches}\)

You can also find the circumference of a circle using the diameter (​d​). The diameter of a circle is two times the radius. The formula to calculate the circumference using a circle's diameter is

\(P=\pi d\)

​Volume:​ The volume (​V​) of most objects can be found by multiplying the base area (​A​) by height (​h​).

Step 1

Record the length (​l​), width (​w​), and height (​h​) of a square or rectangle. Use the formula

\(V=l\times w\times h=A\times h\)

to solve for the volume (​V​). In this formula, the base area (​A​) can be found by multiplying the length (​l​) by the width (​w​). For example, a box measuring 3 feet long, 1 foot wide and 5 feet high has a volume of

\(V=3\times 1\times 5 = 15\text{ ft}^3\)

The box is 15 cubic feet.

Step 1

Use the formula

\(V=\frac{1}{3}Ah\)

to find the volume of a pyramid. For example, for a pyramid with a base area (A) of 25m² and a height of 7m

\(V=\frac{1}{3}(25)(7)=58.3\text{ m}^3\)

The volume of the pyramid is 58.3 cubic meters or 58.3 meters cubed.

Step 1

For a cylinder with a circular base, use the formula

\(V=Ah=\pi r^2 h\)

to solve for the volume of a cylinder. For example, a cylinder with a radius of 2 meters and a height of 5 meters will have a volume of

\(V=\pi(2)^2(5)=62.8\text{ m}^3\)

The volume of the cylinder is 62.8 cubic meters or 62.8 meters cubed.

Calculating Area, Perimeter, and Volume

Calculating the area, perimeter, and volume of simple geometric shapes can be found by applying some basic formulas. It is a good idea to learn and understand what they are and commit those formulas to memory.