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Area of Rectangles
1.
5. Draw a rectangle with an area
of 8 square units.
Area =
6.
Draw a rectangle with an area
of 16 square units.
2.
7. Draw a rectangle with an area
of 20 square units.
Area =
3.
Area =
8. Draw a rectangle with an area
of 20 square units that is
different from the one above.
4.
Area =
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Student Materials Page 1 of 15
Area of Rectangles
1. Cut out the square and standard ruler at the bottom of the page. Use these measurement
tools to help determine the area of the rectangles A, B, C and D.
A
Area =
Area A =
B
Area B =
C
Area C =
Cut out these measurement tools:
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Student Materials Page 2 of 15
2. Explain how to determine the number of 1 x 1 squares that will fit in this rectangle. Can
you do it two ways?
D
Explanation:
3. Select one side of the rectangle as the base. How many unit squares would fit on that
base? How many rows would fill the rectangle?
Base =
4
Rows =
Area =
8
4. Determine the area of the following rectangles.
determined your answer.
4
5
Be prepared to explain how you
18
8
20
2.5
Area =
Area =
Area =
5. Explain how to determining the area of any rectangle using the words base and height.
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Student Materials Page 3 of 15
Bases and Heights
There are specific rules for naming the bases and heights of rectangles, parallelograms and
triangles.
•
The base of a shape can be any side of the shape you choose!
•
For the side you choose to call the base, there is only one option for the height! The
height is the distance perpendicular to the base.
For Example:
Here are three copies of the same triangle. In each example, a different side has been chosen as
the base. Notice that the height changes depending on which side is called the base!
height
height
height
base
base
base
For each shape below, one side has been chosen as the base.
Draw and label the height for each shape.
C
A
B
base
base
base
D
E
base
base
base
F
base
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G
H
base
Student Materials Page 4 of 15
Area of Parallelograms
1. Determine the area of the parallelograms.
A
B
C
D
2. Complete the table showing the base, height and area of parallelograms A, B, and C.
Parallelogram
Base
Height
Area
A
B
C
D
3. Explain how to determine the area of any parallelogram using the words base and height.
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Student Materials Page 5 of 15
Area of Triangles
Directions:
•
Carefully cut out each triangle so that you have two identical copies of each triangle.
•
Secure each pair of identical triangles together with tape to create 3 parallelograms.
A
A
Base
B
B
Base
C
C
Base
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Student Materials Page 6 of 15
Area of Triangles
Directions:
•
•
Tape the parallelograms you created onto the grid so that the corners of the shape touch the
grid corners.
Use the grid to help you determine the base, height and area of each triangle and
parallelogram. Record your answers in the table below.
Base
Height
Area of Parallelogram
Area of Triangle
Shape A
Shape B
Shape C
Explain how the area of a triangle is related to the area of a parallelogram with the same base
and height.
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Student Materials Page 7 of 15
Area Formulas Summary
Summarize what you have learned about finding the area of rectangles, parallelograms and
triangles by writing formulas and drawing diagrams.
Area of ANY Rectangle or Parallelogram
Write a formula that can be used to
rectangle or parallelogram using the base and height.
Use the letters:
A = Area
B = Base
determine
the
area
of
any
H = Height
Make a diagram showing how to find
Label the base and height dimensions in your diagram.
the
area
of
a
parallelogram.
Area of ANY Triangle
Write a formula to find the area of any triangle using the base and height.
Use the letters:
A = Area
B = Base
H = Height
Make
a
diagram
showing
how
to
find
Label the base and height dimensions in your diagram.
the
area
of
any
triangle.
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Student Materials Page 8 of 15
Area Practice
Find the area of the following shapes. Beware…in some cases, more information may be given
than is needed to find the area of the shape!
1.
4.
6
4
5
6
7
5.
6
2.
12
8
8.2
5
7
6.
10
7
3.
9
9.5
7.
6.5
3
2
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Student Materials Page 9 of 15
Painting Sidewalks
It's difficult to imagine a world without color, and who would want to? It's the
vibrant blues, vivid greens, and glowing oranges that add interest and beauty to the
earth. Sure, black, white and gray have their place in the world—but alone they are
boring and dull. We need a burst of color to spice things up a bit.
Imagine for a moment we could add colors to ordinarily bland things. For
instance, wouldn't it be exciting if construction companies added some dye to concrete?
Just imagine walking along flaming red sidewalks or leaning against a baby blue wall.
If we decide to add some color to the bland areas of the world, we’re going to
need to know exactly how much area needs to be colored. In this activity, you will use
what you know about the area of rectangles, parallelograms and triangles to create your
own design for coloring a sidewalk.
Text adapted from the article, Life Could Use Infusion of Color, by Lynn Kargol, http://www.easternecho.com March
13, 2006
Let’s start with an ordinary sidewalk. Below is a diagram showing a typical sidewalk.
6 feet
32 feet
What are the dimensions of one sidewalk rectangle?
?
?
1. Base =
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feet
Height =
feet
Student Materials Page 10 of 15
Remember that area is the amount of space needed to cover a flat shape.
Squares
are the basic unit for measuring area, so we say that area is measured in square units,
such as square inches or square feet.
For example: a square foot is the area inside a square with sides 1 foot long.
1 foot
Area = 1 square foot
1 foot
To visualize the area of the sidewalk section, it is sometimes helpful to divide the
sidewalk section into squares. Here is an enlarged picture of one sidewalk section.
Each small square represents 1 square foot.
One Section of Sidewalk
2. What is the total area of this section of sidewalk?
3. What are the units for the area of the sidewalk?
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Student Materials Page 11 of 15
Here is another picture of the section of sidewalk.
One Section of Sidewalk
6 feet
8 feet
4. How could you use the dimensions of 6 and 8 to calculate the area of the sidewalk
without counting squares?
Here is a larger sidewalk made out of the 4 smaller sections shown below.
6 feet
32 feet
5. Explain how you can determine the area of the entire sidewalk above.
6. If you know the base and height of any rectangle, explain how you can find the area
of the rectangle.
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Student Materials Page 12 of 15
Now that we’ve refreshed our understanding of how to find area, let’s think back
to our original plan of coloring the sidewalk. For example, suppose we decide to color
the sidewalks surrounding our school. We have equal amounts of weather-resistant
paint in two different colors and we need to decide on a design for painting that will use
equal amounts of each color.
Think of one design option for painting the sidewalk rectangles so that equal
amounts of each paint color are used. Label the diagram below so that the painters will
know which areas to use which color paint.
7. Describe how you know that equal areas will be painted each color.
Painting rectangles is fun and definitely adds some color to the world.
Let’s get a bit
more creative. Another idea for painting the sidewalk is to divide each rectangle into
triangles to get a more interesting design. Here is one design option:
6 feet
8 feet
8. Explain how you can determine the area of each triangle.
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Here is another design option made by dividing the sidewalk section into triangles.
9. Explain how you can determine the area of each triangle in this design.
Now it’s time to have some fun. Your task is to create a design for the sidewalk around
our school. You may be as creative as you want, but you must follow these guidelines:
1. You get to design a section of sidewalk that measures 6 ft by 8ft. Your design
must be drawn carefully with a ruler so that lines are straight on the grid.
2. Your sidewalk sections should be painted using 2 colors. Use colored pencils to
show which areas are to be painted which colors.
3. Divide the sidewalk sections into rectangles, parallelograms and triangles to
create an interesting and unique design. There is no limit to how you can design
your sidewalk – but for the purposes of this assignment, you must include at least
one triangle, one parallelogram, and one rectangle in your design.
4. When your design is complete, you must determine exactly how much area is
painted each color.
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Student Materials Page 14 of 15
Sidewalk Design
When your design is complete, you need to determine how much area you have painted
each color.
• Label each region in your design with a letter.
• Show how you compute the area of each region in the work space below.
• Find the total area of each color.
Color:
Color:
Show all work here:
Show all work here:
Total Area Painted:
Total Area Painted:
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Student Materials Page 15 of 15