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.
Move the four vertices to make your own trapezoid
in the following diagram.
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.
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 =
Add the areas of these two triangles, and simplify the expression.
What do you get?