Lesson 2: Area - Trapezoid Examples

The formula for the area of a trapezoid is:

\(\begin{align} \text{Area}_{\text{trapezoid}}&=\frac{\left(a+b\right)\times \text{height}}{2} \\ \\ \text{A}_{\text{trapezoid}}&=\frac{\left(a+b\right)h}{2} \\ \end{align}\)

In this formula, a and b are the lengths of the parallel sides. When using a formula to calculate area, follow these basic steps:

  1. State the formula being used to solve the problem.
  2. Substitute known values for the variables.
  3. Solve for the unknown (remember to include proper squared units in your answer).

Remember that with all area calculations, all dimensions must be in the same unit of measure prior to substituting their values into the formula.

   Multimedia

A video demonstrating a solution to calculating the area of a trapezoid is provided.



EXAMPLE 1

Determine the area of the trapezoid shown.



Solution


\(\begin{align} \text{A}_{\text{trapezoid}}&=\frac{\left(a+b\right)h}{2} \\ \\ &=\frac{\left(25\,\text{cm}+55\,\text{cm}\right)20\,\text{cm}}{2} \\ \\ &=\frac{80\,\text{cm}\times 20\,\text{cm}}{2} \\ \\ &=800\,\text{cm}^2 \\ \end{align}\)

The area of the trapezoid is 800 cm2.

EXAMPLE 2

In the NHL, there is a restricted area for goaltenders behind their own net which is trapezoidal in shape. The trapezoid measures 11 feet from the boards to the goal line, 18 feet along the goal line, and 28 feet along the boards. Each of the angled lines from the goal line to the boards is 12 feet long. What is the area of the trapezoid?

Solution


When no diagram is provided, the initial step is to draw a diagram. In the question, there is more information than is needed to solve the problem. The length of the lines that go from the goal line to the boards are not needed to solve for the area, so it is not necessary to include them on the diagram.



Once the diagram is complete, follow the general steps for solving area problems.

\(\begin{align} \text{A}_{\text{trapezoid}}&=\frac{\left(a+b\right)h}{2} \\ \\ &=\frac{\left(18\,\text{ft}+28\,\text{ft}\right)11\,\text{ft}}{2} \\ \\ &=253\,\text{ft}^2 \\ \end{align}\)

The area of the trapezoid in an NHL arena is 253 ft2.


Now, it is your turn! Complete the questions in your Chapter 7, Lesson 2 Practice Makes Perfect that refer to Area of Trapezoids.



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