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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. A 30 Second Look-See. Read the top of page 315

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The rectangle method

The Rectangle Method

Finding Area of Triangles and Parallelograms


A 30 second look see

Find something in the room shaped like:

  • a hexagonal prism

  • a cylinder

  • a quadrangle

  • a cube

A 30 Second Look-See


Math journal page 315

  • 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.

Math Journal page 315


Rectangle method

Rectangle Method


Add the parts
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.


The rectangle method

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.


The rectangle method

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.


3 units 12 units 15 units

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 units




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


The rectangle method

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
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 table1
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 each rectangle by multiplying the base x height

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.


The rectangle method

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 7 12 units

4 ½ units will this information help us to find the area of the triangles?

7 ½ units

4 ½ + 7 ½ = 12 units


Review your work

  • 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.

Review your work




Find the area of the yellow and blue triangles use the rectangle method mentally1

7 ½ units rectangle method mentally.

5 units

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



The rectangle method
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.


The rectangle method

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 work1
Review your work rectangle and subtract the 12 ½ units of the blue and yellow triangles.


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




Determine the areas of the three shapes and add the parts1

1 x 6 = 6 of this shape.

6 ÷ 2 = 3

= 3 units

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


Determine the areas of the three shapes and add the parts2

1 x 6 = 6 of this shape.

6 ÷ 2 = 3

= 3 units

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


Determine the areas of the three shapes and add the parts3

6 x 4 = 24 units of this shape.

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


3 3 24 30 units

24 units of this shape.

= 3 units

= 3 units

3 + 3 + 24 = 30 units


Review your work2

  • 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.

Review your work


Practice with a partner

Practice with a Partner


Practice on your own

Practice on Your Own