How to Solve Rectangle and Square Problems

A cube is a square taken to the third dimension.

The most basic classroom exercises that involve applying mathematics to rectangles and squares commonly call for calculations of the figure's total area or its perimeter. Rectangles and squares have more in common than four sides and four angles. You can use the same mathematical formulas to solve basic problems like perimeter and areas for both rectangles and squares. If you take things into the third dimension, you can also calculate the volume of either a square or rectangular box with just one formula.

Instructions

Calculate Area

1. Measure or calculate the lengths of any two adjoining sides on the rectangle or square.

2. Check that the lengths of the sides are measured in the same unit of measure. If the sides are measured in different units, perform the necessary conversions to deal with just one unit of measure. For example, if you know one side of a rectangle is 5 inches and the other is 1 foot long, you can convert the "1 foot" measurement to 12 inches.

3. Multiple the lengths of the two sides together. To continue the example, this gives you 5 * 12 = 60 as a result.

4. Label the result with the original units of measure squared, or place a superscript 2 immediately after the unit of measurement. This indicates that the figure applies to a two-dimensional measurement.

Calculate Perimeter

1. Add the lengths of all four sides of the square or rectangle together. The result is the perimeter. If you don't have the lengths of all four sides, measure or calculate the lengths of any two adjacent sides.

2. Perform any necessary conversions so that both sides are in the same unit of measurement.

3. Multiply each side's measurement by 2. If you use the same rectangle example from the area calculations, with a known 5-inch side and a known 12-inch side, you'd have 5 * 2 = 10 inches for one result, and 12 * 2 = 24 inches for the other figure.

4. Add the two figures together. To continue the example, you have 10 + 24 = 34 inches as your result. Label it with the same unit of measurement the sides were originally measured in. Because you're calculating the distance around the square or rectangle in just one dimension -- length -- your answer is in simple units, not units squared.

Calculate Volume

1. Measure the length, width and height of the box, cube or rectangular shape.

2. Check that all three measurements are in the same unit of measure. Make any conversions necessary to achieve this.

3. Multiply all three measurements together. For example, if the box has a 5-inch-by-12-inch footprint -- the same as the rectangle from the other examples -- and is 4 inches high, you'd have 5 * 12 * 4 = 240.

4. Label the result with the original unit of measurement. Add "cubed" after the measurement, or use a superscript 3 to indicate that the measurement applies to three-dimensional space.

References

• Math is Fun: Area of Plane Shapes