 WME@Kimpton Middle

## Area of a Trapezoid You already know how to find the area of a triangle. Now we will consider the area of a trapezoid.

The diagram on the right shows a typical trapezoid with its two parallel sides and its two arbitrary sides. The height is the distance between the parallel sides.

Take any trapezoid draw a diagonal to get two triangles. Add their areas up and you get the area of the trapezoid. This is the key to finding the area of a trapezoid.

1. Move the four vertices to make your own trapezoid in the following diagram.

2. In the above diagram, draw a diagonal (click the button). Now you have the trapezoid cut into two triangles: ABC and ADC. And it is neat to observe that the area of the trapezoid can be gotten by adding the areas of the two triangles together.

3. Now, draw the height of the trapezoid (click the button) whose length will be denoted by h. Use this diagram to answer the following questions.

• Move the height to the point A. What does this tell you about the height of the upper triangle? It is (enter a symbol):

• The base of the upper triangle is (enter an edge):

• Move the height to the point C. What does this tell you about height of the lower triangle? It is (enter a symbol):

• The base of the upper triangle is (enter an edge):

• The area of the upper triangle is:  ×   / 2 =

• The area of the lower triangle is:  ×   / 2 =

4. Add the areas of these two triangles, and simplify the expression. What do you get?

5. Now it is time to