# Area of Trapezoids

In these lessons we will learn

• how to find the area of trapezoids
• how to derive the area formula of a trapezoid
• how to solve problems using area of trapezoids

What is a trapezoid?
A trapezoid is a 4-sided polygon with two parallel sides. A trapezoid is also called a trapezium (UK English).

How to find the Area of a Trapezoid?

Given that side a is parallel to side b and h is the vertical height between a and b, the area of the trapezoid is given by the formula:

Example:
Find the area of the following trapezoid:

Solution:
Area of trapezoid

How to find the height of a trapezoid given the area?

Example:
Given that the area of the following trapezoid is 36. Find the value of h.

Solution:

Worksheet to calculate the area of trapezoids.

Worksheet to solve trapezoid problems involving base1, base2, height and area.

How to find the area of a trapezoid using the formula 1/2(a + b)h?
Step 1: Find the bases and height. (The height must be perpendicular to bases)
Step 2: Add the bases and multiply by the height.
Step 3: Divide the answer by 2.
Step 4: Write the units.

Find the area of trapezoid

Find the height of a trapezoid given its area
Find the height of the trapezoid shown below, if the area is 378.56

### Derive the area formula of a trapezoid

How to derive the area formula of trapezoid by using the area of triangles?
How to derive the area formula for a trapezoid using either two triangles or a parallelogram?

### Problems involving area of trapezoid

The following video shows a problem involving the area of a trapezoid.

Example:
The area of a trapezoid is 91 and the height is 14.One of the bases has a length of 10. Find the length of the other base.

Example:
The area of a trapezoid is 220 sq. ft. The length of the bases are 10 and 45 ft. Find the height/altitude of the trapezoid.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.