Concept Byte: Transforming to Find Area

Use With Lessons 10-1 and 10-2

ACTIVITY

You can use transformations to find formulas for the areas of polygons. In these activities, you will cut polygons into pieces and use the pieces to form different polygons.

Activity 1

• Step 1 Count and record the number of units in the base and the height of the parallelogram below.
• Step 2 Copy the parallelogram onto grid paper.
• Step 3 Cut out the parallelogram. Then cut it into two pieces as shown.
• Step 4 Translate the triangle to the right through a distance equal to the base of the parallelogram.

The translation results in a rectangle. Since their pieces are congruent, the parallelogram and rectangle have the same area.

1. How many units are in the base of the rectangle? The height of the rectangle?
2. How do the base and height of the rectangle compare to the base and height of the parallelogram?
3. Write the formula for the area of the rectangle. Explain how you can use this formula to find the area of a parallelogram.

Activity 2

• Step 1 Count and record the number of units in the base and the height of the triangle below.
• Step 2 Copy the triangle onto grid paper. Mark the midpoints A and B and draw midsegment A B ¯ . eh b bar , .
• Step 3 Cut out the triangle. Then cut it along A B ¯ . eh b bar , .
• Step 4 Rotate the small triangle 180 ° 180 degrees  about the point B.

The bottom part of the triangle and the image of the top part form a parallelogram.

4. How many units are in the base of the parallelogram? The height of the parallelogram?

Table of Contents