# How to Find the Area of a Trapezoid (Mathematics Lesson)

# How to Find the Area of a Trapezoid

The area of a trapezoid is found using the formula:In this formula,

**b**and

_{1}**b**are the lengths of the bases of the trapezoid and

_{2}**h**is the height of the trapezoid. The image below shows what we mean by the lengths of the bases and the height:

# A Real Example of How to Find the Area of a Trapezoid

#### An Example Question

What is the area of a trapezoid with bases of length 3 cm and 5 cm and a height of 2 cm, as shown below?Step 1

Start with the formula:
Area = ½(b

_{1}+ b_{2})h**Don't forget:**½(b

_{1}+ b

_{2})h = ½ × (b

_{1}+ b

_{2}) × h

Step 2

Substitute the length of the bases and the height into the formula. In our example, b_{1}= 3, b

_{2}= 5 and h = 3.

Area = ½ × (3 + 5) × 2

Area = ½ × (8) × 2

Area = 8 cm

Area = ½ × (8) × 2

Area = 8 cm

^{2}**Don't forget:**Calculate what's in the brackets () first (using the order of operations). In our example, (3 + 5) = 8

**or:**½ × a number = 0.5 × a number = a number ÷ 2.

The area of a trapezoid with bases of length 3 cm and 5 cm and a height of 2 cm is 8 cm

^{2}.

# Another Real Example of How to Find the Area of a Trapezoid

The slider below shows another real example of how to find the area of a trapezoid:##### Curriculum

##### Interactive Test

**show**

Here's a second test on finding the area of a trapezoid.

Here's a third test on finding the area of a trapezoid.

##### Note

# Trapezoid, Trapezium

The shape is called a trapezoid in North America.In English speaking countries outside North America, a trapezoid is called a

**trapezium**.

# What Is a Trapezoid?

A trapezoid is a four-sided flat shape with straight sides. It has a pair of opposite sides which are parallel.# A Note on Units

The area of a trapezoid is a length times a length, so we say its dimension is length^{2}. (All areas are lengths squared.)

This affects the units used. If the lengths of a rectangle are in cm, the area is in cm

^{2}. If the lengths are in inches, the area is in inches

^{2}.