How to Calculate Area, Perimeter and Volume

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The ability to calculate 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 you can calculate any of these parameters.

Area

    Record the length and width of a square or rectangle. Substitute your measurements into the formula "length x width" to solve for area. For example, a rectangle with a length of 7 meters (m) and a width of 3m has an area of: 7m x 3m = 21m^2 (21 meters squared, or 21 square meters).

    Use the formula "(base x height)/2" to find the area of a triangle. A triangle with a height of 7m and a base of 3m has an area of 7m x 3m = 21m^2, divided by two equals 10.5m^2.

    Multiply pi (3.14) by the square of the radius (πr2) to solve for the area of a circle. For example, a circle with a radius of 5 inches will have an area of 3.14 x (5 x 5) = 78.5 square inches.

Perimeter

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

    Add the measurements to get the value of the perimeter. For example, a rectangle has two sides measuring 6 feet and two sides measuring 4 feet. The perimeter is: 6 + 6 + 4 + 4 = 20 feet.

    Use the formula "pi x (2 x radius)" to find the perimeter, or circumference, of a circle. For example, a circle with a radius of 3 inches has a circumference of 3.14 x (2 x 3) = 18.8 inches. You can also find the circumference of a circle with the formula "pi x diameter."

Volume

    Record the length, width and height of a square or rectangle. Use the formula "length x width x height" to solve for the volume. For example, a box measuring 3 feet long, 1 foot wide and 5 feet high has a volume of 3 x 1 x 5 = 15 cubic feet.

    Use the formula "(1/3) x b x h" to find the volume of a pyramid. In this formula, "A" is the base area of the pyramid, and "h" is the height of the pyramid. For example, for a pyramid with a base area of 25m^2 and a height of 7m, the volume is (1/3) x 25 x 7 = 58.3 cubic meters.

    Use the formula "πr2 x 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 3.14 x (2 x 2) x 5 = 62.8 cubic meters.

References

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