Use this dynamic worksheet to answer the questions that follow and determine the equation for the area of any trapezoid.

1. Start by clicking on the "Show variables" check box to make sure we're using the same terms. No other variables should be part of the equation you derive. When finished, uncheck the "Show variables" check box.

2. Click on the "Show dimensions" check box to display the lengths of the diagonals. Can you determine the area of the trapezoid?

3. Click on the "Show midpoints" check box. A Rotation slider appeared. Slide the slider all the way to the right. Can you express the formula for that new figure in terms of the variables already shown? (Hint: What is the length of the entire figure after rotation? What is its width?)

4. Can you determine the area of the trapezoid? If not, you may find it helpful to review the rectangles worksheet. If so, continue to step 5 and test your conjecture.

5. Experiment by doing the following several times:
a) uncheck the "Show area" and "Show midpoints" check boxes;
b) adjust the dimensions of the trapezoid by sliding the height and corner sliders (labeled Height, UpperLeft, UpperRight, LowerLeft, and LowerRight);
c) click on the "Show dimensions" check box to see the dimensions of the trapezoid you've created;
d) calculate the area on your own using the values of the variables "b_1" (first base) and "b_2" (second base), and "h" (height);
e) check the "Show area" check box to verify;
f) click on the reset button in the upper right hand corner to reset this construction before repeating.

6. When you are satisfied, write down the equation for area in terms of base and height. Check your answer by checking the "Show equation" check box. If you have difficulty, raise your hand so your teacher can help.

Take the quiz!

Go to: Rhombus, Kite

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