 # Area of Trapezoids

Related Topics: More Geometry Lessons
Geometry Worksheets

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
How to use the area of a trapezoid to find a missing base length?

### Derive the area formula of a trapezoid

The following video shows how to derive the area formula for a trapezoid using either two triangles or a parallelogram. How to derive the area formula of trapezoid by using the area of triangles?

### 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.

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