Area of Trapezoid Formula

This figure illustrates the area of a trapezoid formula.

Formula

Summary

The area of a trapezoid is given by the sum of its base and top length multiplied by its height.

Expression Description
The area of the trapezoid.
The length of the top of the trapezoid.
The length of the base of the trapezoid.
The height of the trapezoid

Usage

The area of a trapezoid is given by its height multiplied by the sum of its top length and bottom length divided by two.

Examples

Example 1

area of trapezoid top 3 base 5 height 2

This example demonstrates how to find the area of a trapezoid with a top of 3 a base of 5 and a height of 2.

Steps

  1. Start by setting up the formula.

  2. Substitute the values for the top, base and height into the formula.

  3. Evaluate the addition.

  4. Simplify by performing multiplication then division or using another way.

  5. The area of the trapezoid is equal to units squared.

Example 2

area of trapezoid top 5 base 8 height 4

This example demonstrates how to find the area of a of trapezoid top 5 base 8 height 4.

Steps

  1. Start by setting up the formula.

  2. Substitute the values for the top, base and height into the formula.

  3. Evaluate the addition.

  4. Simplify the numerator and denominator.

  5. The area of the trapezoid is equal to units squared.

Example 3

area of trapezoid top 4 base 7 height 3

This example demonstrates how to find the area of a of trapezoid top 4 base 7 height 3.

Steps

  1. Start by setting up the formula.

  2. Substitute the values for the top, base and height into the formula.

  3. Evaluate the addition.

  4. Evaluate the division.

  5. The area of the trapezoid is equal to units squared.

Explanation

The formula for the area of a trapezoid can be derived using an observation and the formula for the area of a parallelogram[1].

References

  1. Derive Area of Trapezoid Formula
    Wumbo (internal)