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

1. Start by clicking on the "Show variables" check box. Since we're going to derive the formula, let's 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 kite?

3. Slide the Rotate slider all the way to the right. What is the shape of the entire figure? 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. Slide the Rotate slider towards the middle. Can you see how much of the entire figure is made up of the kite? How do you know?

5. If you were able to determine the area of the entire figure, how much of that area is made from the kite?

6. Can you determine the area of the kite? If not, you may find it helpful to review the rectangles worksheet. If so, continue to step 7 and test your conjecture.

7. Experiment by doing the following several times:
a) uncheck the "Show area" check box;
b) click on any of the points in blue and drag them around to change the shape of the kite;
c) slide the Rotate slider to see that a kite's relation to a rectangle of the same dimensions is constant;
d) click on the "Show dimensions" check box to see the dimensions of the kite you've created;
e) calculate the area on your own using the values of the variables "d_1" (first diagonal) and "d_2" (second diagonal);
f) check the "Show area" check box to verify;
g) click on the reset button in the upper right hand corner to reset this construction before repeating.

8. When you are satisfied, write down the equation for area in terms of its diagonal lengths, d_1 and d_2. 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, Quadrilateral Test,  Real World Problem

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