 Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum            Session 6, Part B:
Exploring Area With a Geoboard

In This Part: Subdividing Area | The Rectangle Method | Formulas | The Triangle Formula

Why does the formula A = work for triangles other than right triangles? To answer this question, let's look at parallelograms, since we'll derive the triangle formula from the formula for the area of a parallelogram.  Problem B7 a. Explain how the area of a parallelogram with height a and base b (as shown below) is found using the formula A = a • b. How does it compare to the area of a rectangle with the same height and base? b. Examine the figure below, in which two congruent triangles are placed together to form a parallelogram. Using this figure, explain how the formula for the area of a triangle relates to the formula for the area of a parallelogram.   Note the height of the triangle, h, is the length of the line segment perpendicular to the base and adjoining it to the opposite vertex. This is equal to the height of the parallelogram.   Close Tip Note the height of the triangle, h, is the length of the line segment perpendicular to the base and adjoining it to the opposite vertex. This is equal to the height of the parallelogram.      Problem B8 Make a parallelogram out of two trapezoids as follows:

 • Fold a piece of paper in half. • Draw any trapezoid on the piece of paper. • Label the top base b1, the bottom base b2, and the height h. • Cut out two identical copies of your trapezoid, and arrange them to form a single parallelogram.
 a. What is the area of this parallelogram? b. How does the area compare to the area of a single trapezoid? What is the area of one trapezoid?  Next > Part C: Scaling the Area  Session 6: Index | Notes | Solutions | Video