```Lanier Middle School
“An International Baccalaureate Middle Years Programme School”
7th – LESSON 9.4 Composite Figures
Daily Objective: How do you find the area of composite figures?
Describe one way you can find the area of the garden shown on
the right.
1
Use dotted lines to show two different ways the garden
cold be divided up into simple geometric figures.
Find the areas of each of the following figures.
2
A composite figure is made up of simple geometric
shapes. To find the area of a composite figure or other
irregular-shaped figure, divide it into simple,
nonoverlapping figures. Find the area of each simpler
figure, and then add the areas together to find the total
area of the composite figure.
Use the chart below to review some common area
formulas.
3
5
A banquet room is being carpeted. A floor plan of the
room is shown at the below. Each unit represents 1 yard.
The carpet costs \$23.50 per square yard. How much will
it cost to carpet the room?
4
Find the area of the figure below
Lanier Middle School
“An International Baccalaureate Middle Years Programme School”
6
A window is being replaced with tinted glass. The plan below
shows the design of the window. Each unit length represents 1
foot. The glass costs \$28 per square foot. How much will it cost
to replace the glass? Use 3.14 for pi.
8
Calculate the area of the composite figure shown below.
10
A banner is made of a square and a semicircle. The square has
side lengths of 26 inches. One side of the square is also the
diameter of the semicircle. What is the total area of the banner?
Use 3.14 for pi.
11
Erin wants to carpet the floor of her closer. A floor plan of the
closet is shown below.
7
A tile installer plots an irregular shape on grid paper.
Each square on the grid represents 1 square centimeter.
What is the area of the irregular shape?
9
Sal is tilling his entryway. The floor plan is drawn on a
unit grid. Each unit length represents 1 foot. Tile costs
\$2.25 per square foot. How much will Sal pay to file his
entryway?
12
Hexagon ABCDEF has vertices A(-2,4), B(0,4), C(2,1),
D(5,1), E(5,-2), and F(-2,-2). Sketch the figure on a
coordinate plante. What is the area of the hexagon?
13
A field is shaped like the figure shown below. What is
the area of the field? Use 3.14 for pi.
How much carpet does Erin need?
The carpet Erin has chosen costs \$2.50 per square foot. How
much will it cost to carpet the floor?
14
A bookmark is shaped like a rectangle with a semicircle attached
at both ends. The rectangle is 12 cm long and 4 cm wide. The
diameter of each semicircle is the width of the rectangle. What is
the area of the bookmark? Use 3.14 for pi.
16
A composite figure is formed by combining a square and a
triangle. Its total area is 32.5 square feet. The area of the triangle
is 7.5 square feet. What is the length of each side of the square?
15
Alex is making 12 pennants for the school fair. The
pattern he is using to make the pennants is shown in the
figure. The fabric for the pennants costs \$1.25 per square
foot. How much will it cost Alex to make 12 pennants?
Lanier Middle School
“An International Baccalaureate Middle Years Programme School”
17
Christina plotted the shape of her garden on graph paper. She
estimates that she will get about 15 carrots from each square unit.
She plans to use the entire garden for carrots. About how many
carrots can she expect to grow?
18
The figure shown is made up of a triangle and a square.
The perimeter of the figure is 56 inches. What is the area
of the figure? Explain
19
The pattern for a scarf is shown at the right. What is the area of
the scarf? Use 3.14 for pi.
20
The design for the palladium window shown includes a
semicircular shape at the top. The bottom is formed by
squares of equal size. A shade for the window will
extend 4 inches beyond the perimeter of the window,
shown by the dashed line around the window. Each
square in the window has an area of 100 square inches.
What is the area of the window? Use 3.14 for pi.