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The Rectangle Method

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The Rectangle Method

Finding Area of Triangles and Parallelograms

Find something in the room shaped like:

- a hexagonal prism
- a cylinder
- a quadrangle
- a cube

- Read the top of page 315
- Your job will be to think of ways to find the areas of the triangles – I am not interested in the answer.
I am interested in the methods you

and your partner discover.

- This is called the rectangle method because rectangles are used to surround the figure or parts of the figure. All of the areas that are calculated are either areas of rectangles or of triangular halves of rectangular regions.

Split this triangle up into two different triangles, both with right angles, count the units that cover each and find the sum of the two parts.

12 units

3 units

Split this triangle up into two different triangles, both with right angles, count the units that cover each and find the sum of the two parts.

12 units

3 units

12 units

3 units

9 units

15 units

9 ÷ 2 =

4 ½ units

15 ÷ 2 =

7 ½ units

4 ½ units

7 ½ units

- Return to page 315.
- Find the area of triangle #1 by splitting the triangle into two right triangles. Use the add the parts method to find the area of the complete triangle.

7 ½ units

5 units

The difference will be the area of the red triangle.

15 units – 12 ½ units = 2 ½ units.

1 x 6 = 6

6 ÷ 2 = 3

= 3 units

1 x 6 = 6

6 ÷ 2 = 3

= 3 units

6 x 4 = 24 units

24 units

= 3 units

= 3 units

- Return to page 315.
- Find the area of triangle #3 by splitting the parallelogram into two right triangles and a rectangle. Use the add the parts method to find the area of the complete parallelogram.

- Math Journal page 316

- Math Sheet p. 126