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
• 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
• 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
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
3 units + 12 units = 15 units
Using 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
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.
9 units
Find the area of each rectangle by
multiplying the base x height.
15 units
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 ½ units
7 ½ units
4 ½ + 7 ½ = 12 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.
Review your work
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
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.
To find the area of the red triangle, find the
area of the rectangle and subtract the 12 ½
The difference will be the area of the red triangle.
units of the blue and yellow triangles.
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 work
Area of a Parallelogram
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.
1x6=6
6÷2=3
= 3 units
Determine the areas of the three
shapes and add the parts.
1x6=6
6÷2=3
= 3 units
Determine the areas of the three
shapes and add the parts.
6 x 4 = 24 units
Determine the areas of the three
shapes and add the parts.
24 units
= 3 units
= 3 units
3 + 3 + 24 = 30 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.
Review your work
• Math Journal page 316
Practice with a Partner
• Math Sheet p. 126
Practice on Your Own