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Trapezoid Area: Formula & Examples

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Trapezoid Area: Formula & Examples

A trapezoid is a quadrilateral with at least one pair of parallel sides. These parallel sides are called bases, and the other two sides are called legs. To calculate the area of a trapezoid, we use the following formula:

Formula for Trapezoid Area

Area = (1/2) * (sum of bases) * height

Where:

  • Area: The amount of space enclosed within the trapezoid.
  • Bases: The lengths of the parallel sides of the trapezoid (b1 and b2).
  • Height: The perpendicular distance between the two bases.

Step-by-Step Calculation

To find the area of a trapezoid, follow these steps:

  1. Identify the bases: Determine the lengths of the two parallel sides.
  2. Determine the height: Find the perpendicular distance between the bases. This can be measured from any point on one base to the opposite base.
  3. Apply the formula: Substitute the values of the bases and height into the area formula.
  4. Calculate the area: Simplify the expression to find the area of the trapezoid.

Examples

Let’s look at some examples to illustrate how to calculate the area of a trapezoid.

Example 1

Imagine a trapezoid with bases of length 6 cm and 8 cm, and a height of 5 cm. To find its area, we follow the steps:

  1. Bases: b1 = 6 cm, b2 = 8 cm
  2. Height: h = 5 cm
  3. Formula: Area = (1/2) * (6 + 8) * 5
  4. Calculation: Area = (1/2) * 14 * 5 = 35 cm2

Therefore, the area of the trapezoid is 35 square centimeters.

Example 2

Consider a trapezoid with bases of 10 inches and 12 inches, and a height of 7 inches. Let’s calculate its area:

  1. Bases: b1 = 10 inches, b2 = 12 inches
  2. Height: h = 7 inches
  3. Formula: Area = (1/2) * (10 + 12) * 7
  4. Calculation: Area = (1/2) * 22 * 7 = 77 inches2

The area of the trapezoid is 77 square inches.

Conclusion

Calculating the area of a trapezoid is a straightforward process using the provided formula. By understanding the formula and following the steps, you can easily determine the area of any trapezoid, whether it’s in a textbook problem or a real-life scenario. Remember, the formula relies on the lengths of the bases and the height of the trapezoid.

Formula