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## PowerPoint Slideshow about ' The Rectangle Method' - renee-donaldson

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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.

Add the Parts 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 with right angles, count the units that cover each and find the sum of the two parts.

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 with right angles, count the units that cover each and find the sum of the two parts.

3 units

3 units + 12 units = 15 unitsUsing the rectangle method, draw a rectangle around each of these triangles.

What observation can you make about these shapes and the shaded regions?

These triangles and ½ of the area of the rectangle. How will this information help us to find the area of the triangles?

12 units will this information help us to find the area of the triangles?

3 units

These triangles and ½ of the area of the rectangle. How will this information help us to find the area of the triangles?Find the area of this triangle with your table. will this information help us to find the area of the triangles?

Find the area of this triangle with your table. will this information help us to find the area of the triangles?

9 units will this information help us to find the area of the triangles?

15 units

Find the area of each rectangle by multiplying the base x height.9 ÷ 2 = will this information help us to find the area of the triangles?

4 ½ units

15 ÷ 2 =

7 ½ units

To find the area of the triangles divide the area of the rectangles by 2 or find the value of ½ the rectangle.4 ½ units will this information help us to find the area of the triangles?

7 ½ units

4 ½ + 7 ½ = 12 units- Return to page 315. will this information help us to find the area of the triangles?
- 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.

To find the area, draw two right angles around the triangle to create a rectangle.

Find the area of the yellow and blue triangles. Use the rectangle method mentally.

7 ½ units rectangle method mentally.

5 units

Find the area of the yellow and blue triangles. Use the rectangle method mentally.The sum of the yellow and blue triangles is 12 ½ units. rectangle method mentally.

To find the area of the red triangle, find the area of the rectangle and subtract the 12 ½ units of the blue and yellow triangles.

The difference will be the area of the red triangle.

15 units – 12 ½ units = 2 ½ units rectangle and subtract the 12 ½ units of the blue and yellow triangles..

If the yellow triangle is 7 ½ units , and the blue triangle is 5 units, does it make sense that the red triangle is 2 ½ units?Review your work rectangle and subtract the 12 ½ units of the blue and yellow triangles.

Area of a Parallelogram rectangle and subtract the 12 ½ units of the blue and yellow triangles.

Use what you know to determine a strategy to find the area of this shape.

Determine the areas of the three shapes and add the parts. of this shape.

1 x 6 = 6 of this shape.

6 ÷ 2 = 3

= 3 units

Determine the areas of the three shapes and add the parts.1 x 6 = 6 of this shape.

6 ÷ 2 = 3

= 3 units

Determine the areas of the three shapes and add the parts.6 x 4 = 24 units of this shape.

Determine the areas of the three shapes and add the parts.- Return to page 315. of this shape.
- 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 of this shape.

- Math Sheet p. 126 of this shape.

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