Most students are comfortable with the basic shapes and formulas taught in middle school math and high school geometry classes. The average person walking down the street can solve for the area of a square or a triangle, but some shapes are more challenging than the basics. One of the most confusing tasks in geometry is solving problems using the area of a trapezoid formula.

Area is the term used to describe the amount of space taken up by a plane or two-dimensional shape. Calculating the area of something is often used to measure how large or small a shape can be. A common example in everyday life is wanting to know how much paint to buy to cover a wall or carpeting a bedroom. There are many formulas to calculate the area, but those vary based on the shape.

A trapezoid is a quadrilateral shape with two parallel sides. The parallel sides are the bases, the non-parallel sides are called legs, and the distance between the two bases is called the altitude. The altitude is sometimes also called the height. There are three types of trapezoids: right trapezoid, isosceles trapezoid, and scalene trapezoid. All types of trapezoids share the same area formula.

### Area of a trapezoid formula:

A is for area

a is for base one

b is for base two

h is for height or altitude

The values for *a *and *b* for the trapezoid bases can be interchangeable. The bases will be added together, divided by 2, and multiplied by the height. The final answer for an area of a shape is always expressed in square units.

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### Example 1:

Find the area of the right trapezoid below.

First, identify and plug in the numbers for your variables.

Simplify.

*A *= 15 inches * 20 inches

*A *= 300 inches^{2}

The area of the right trapezoid is 300 inches^{2}.

### Example 2:

Find the area of the isosceles trapezoid.

Simplify.

*A *= 18.5 in * 7 in

*A *= 129.5 in^{2}

The area of the isosceles trapezoid is 129.5 in^{2}.

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### Example 3:

Find the area of the scalene trapezoid.

Simplify.

*A* = (19 in/2) * 4 in

*A *= 9.5 in * 4 in

*A *= 38 in^{2}

The area of the scalene trapezoid is 38 in^{2}.

### Example 4:

Find the area of a trapezoid given a base of 4 centimeters, a base of 6 centimeters, and a height of 3 centimeters. Note: the units are in centimeters.

First, label your variables with the appropriate numbers. *a is *equal to 4, *b* is equal to 6, and *h* is 3. Plug your numbers into the area of a trapezoid formula.

Follow your order of operations so solve for *A* or the area in inches^{2}.

Simplify.

*A *= 5 centimeters * 3 centimeters

*A *= 15 centimeters^{2}

The area of the trapezoid is 15 cm^{2}.

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### Example 5:

Find the area of a trapezoid given a base of 20 cm, a base of 15 cm, and a height of 10 cm.

Simplify.

*A *= 17.5 cm * 3 cm

*A *= 52.5 cm^{2}

The area of the trapezoid is 52.5 cm^{2}.

While learning and using the area of a trapezoid formula can be stressful, once you have mastered the basics, and added the formula to your personal study guide, you should be able to tackle any question a math teacher sends your way.

Author: Maerie Morales

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