Solving Area Problems
Essential question: How do you find the area of composite figures?
Example 1 – Area of a Composite Figure
Anthony was plotting the shape of his garden on grid paper. While it was an irregular shape,
it was perfect for his yard. Each square on the grid represents 1 square meter.
A) Describe one way you can find the area of this garden.
B) The area of the garden is
square meters.
C) Compare your results with other students. What other methods were used to find the
area?
D) How does your area compare with the area found using different methods?
E) Use dotted lines to show two different ways Aaron’s garden could be divided up into
simple geometric figures.
A composite figure is made up of simple geometric shapes. To find the area of composite
figures and other irregular shaped figures, divide it into simple, non-overlapping figures. Find
the area of each simpler figure, and then add them together to find the total area of the
composite figure.
Use the chart below to review some common area formulas.
Area Formula
Shape
triangle
square
rectangle
parallelogram
trapezoid
A = ½ bh
A = s2
A = lw
A = bh
A = ½ h(b1 + b1)
Example 2 – Finding the Area of a Composite Figure
A) Into what two figures can you divide this composite figure?
B) Find the area of each shape.
Area of the Parallelogram
Area of the Trapezoid
C) Find the area of the composite figure.
+
Area of parallelogram
=
Area of trapezoid
Area of composite shape
D) Describe another way to divide the shape into simpler figures.
E) If you divide the composite figure into different shapes, what is the area? What does this
tell you?
Example 3 – Calculating Cost Based on Area
A living room is being carpeted. A floor plan of the room is shown at below. Each unit length
represents 1 yard. Carpet costs $35.50 per square yard. How much will it cost to carpet the
room?
A) Divide the figure into simpler shapes. Show the divisions on the floor
plan with dotted lines. Count the units to find the dimensions. Label the
dimensions. Then find the area of each of your shapes.
The area of the composite figure is
yd2.
B) To calculate the cost to carpet the room, multiply
The cost to carpet the banquet room is
by the
.
C) Describe how you can estimate the cost to carpet the room.
.
Practice:
Find the area of each figure. SHOW ALL WORK! Use 3.14 for
.
4. Show two different ways to divide the composite figure. Find the area both ways. Show
your work!
5. Shannon is tiling her kitchen. The floor plan is drawn on a unit grid. Each unit length
represents 1 foot. Tile costs $3.25 per square foot. How much will Shannon pay to tile her
kitchen?
6. Reasoning A composite figure is formed by combining a square and a triangle. Its total
area is 32.5 ft2. The area of the triangle is 7.5 ft2. What is the length of each side of the
square?