Skill 48
Calculate the Area of Polygons

Area is how many square units of space are enclosed by the sides of a flat shape. Think of a carpet that takes up a certain amount of space. A room-sized carpet covers more square units of space than a small rug. There are formulas for calculating the area of regular polygon shapes like squares and triangles. On the ASVAB, you are likely to be asked to find the area of a polygon. To do so, you need to memorize a few basic formulas.

Area of a Square or a Rhombus. It is easy to find the area of these polygons. Simply multiply the length of one side by the length of any other side. Because all the sides are equal, you are actually finding the square of one side. So here is the formula for finding the area of a square or a rhombus: area = s² where s is the length of one side. For example, imagine a square with sides that each measure 6 cm. To calculate the area, multiply: 6 cm × 6 cm = 36 cm² (“cm²” is read “square centimeters”).

Always remember that area is indicated in square “units.” The units can be square meters, square miles, square yards, square centimeters, or whatever unit the problem asks for.

Area of a Rectangle or a Parallelogram. To find the area of these shapes, use this formula: area = length × width (also expressed as l × w). In the rectangle and parallelogram below, the area is 90 inches × 20 inches = 1,800 square inches or 1,800 in².

Area of a Triangle. Triangles get a bit more complicated. To find the area of a triangle, use this formula: . The base is the bottom of the triangle. The height is a vertical line from the top of the triangle to the base. Often this line is shown as a dashed line, as in the figure below. (On the ASVAB, if you are asked to find the area of a triangle, the height measurement will be given to you, either in the problem or in a figure.) Look at the triangle below. The base measures 25 ft. The dashed line from the top to the base measures 20 ft. Substitute these numbers into the formula:

Area of a Parallelogram. Now let’s step it up a notch and work with parallelograms. If you think about it, a parallelogram is made up of two triangles. See the figure below.

To calculate the area of a parallelogram, use this formula: or simply base × height (bh). The trick is to identify the base and the height. Look at the triangle on the left (the one with a top that points upward). Its base is the base of the parallelogram. Then draw a line from the top of that triangle down to the base. That line is the height of the parallelogram. (On the ASVAB, if you need to find the area of a parallelogram, you will be given the measurements of these lines.)

Area of a Trapezoid. Finding the area of a trapezoid is a bit more difficult, but not impossible.

To find the area of a trapezoid, use this formula: To calculate, look for the length measure of each of the bases. Then draw the height, which is a line from one of the angles to the opposite base. (On the ASVAB, if you are asked to find the area of a trapezoid, you will be given the height measurement.)

Substitute the measurements from the figure into the formula: base₁ = 12 yd, base₂ = 5 yd, and the height = 3 yd. So area =

Test Yourself!

Jamal wants to paint a wall in his kitchen. The wall measures 12 ft × 20 ft. What is the area of the wall?

If a gallon of paint covers 200 ft², how many gallons of paint will he use?

Tom and Lee need to purchase grass seed for their yard. The yard is the shape of a triangle with a base of 18 m and a height of 12 m. What is the area of the yard?

If grass seed comes in 1 lb packages, and 1 lb is recommended for every 10 m², how many pounds will they need?

How many packages should they buy?

A patio measures 10 ft × 15 ft. What is the area of the patio?

Sammy cuts grass in a neighbor’s yard. The yard is in the shape of a parallelogram and has a height of 56 m and a base of 16 m. What is the area of the yard?

Sammy is cutting the grass in the yard described in the previous question, if he can cut all the grass in 4 hours, how many square meters can he cut in 1 hour?

Sally tiled the floor of her kitchen. The rectangular kitchen measures 14 ft × 28 ft. What is the area of the kitchen floor?

Given the information in Question 6, if Sally took 4 hours to tile the kitchen floor, how many square feet could she tile in 1 hour?

Gina is planting a garden in the shape of a triangle. The height is 4 m and the base is 16 m. What it the area of the garden?

Given the information in Question 8, if Gina can plant 6 tomato plants in every square meter of space, how many tomato plants can she plant?

If a table top measures 5 ft × 6 ft, what is the area?

Given the information in question 10, if Susan purchases a table cloth to cover the table top and to have the cloth hanging over 1 ft on each side, how many square meters must the table cloth be?