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

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The Rectangle Method

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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

  • 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.

Rectangle Method


Add the parts

Add the Parts


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

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

3 units

3 units + 12 units = 15 units


Using the rectangle method draw a rectangle around each of these triangles

Using the rectangle method, draw a rectangle around each of these triangles.


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

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


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

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.


Find the area of this triangle with your table1

Find the area of this triangle with your table.


Find the area of each rectangle by multiplying the base x height

9 units

15 units

Find the area of each rectangle by multiplying the base x height.


The rectangle method

9 ÷ 2 =

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

7 ½ units

4 ½ + 7 ½ = 12 units


Review your work

  • 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.

Review your work


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

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

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


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

7 ½ units

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 units

The sum of the yellow and blue triangles is 12 ½ units.


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.

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


Area of a parallelogram

Area of a Parallelogram


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

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

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


Determine the areas of the three shapes and add the parts1

1 x 6 = 6

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

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

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


3 3 24 30 units

24 units

= 3 units

= 3 units

3 + 3 + 24 = 30 units


Review your work2

  • 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.

Review your work


Practice with a partner

  • Math Journal page 316

Practice with a Partner


Practice on your own

  • Math Sheet p. 126

Practice on Your Own


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