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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.

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Page 1: Example 1 – Area of a Composite Figure · D) Describe another way to divide the shape into simpler figures. E) If you divide the composite figure into different shapes, what is

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.

Page 2: Example 1 – Area of a Composite Figure · D) Describe another way to divide the shape into simpler figures. E) If you divide the composite figure into different shapes, what is

Use the chart below to review some common area formulas.

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

Shape Area Formula

triangle A = ½ bh square A = s2

rectangle A = lw parallelogram A = bh

trapezoid A = ½ h(b1 + b1)

Page 3: Example 1 – Area of a Composite Figure · D) Describe another way to divide the shape into simpler figures. E) If you divide the composite figure into different shapes, what is

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 by the .

The cost to carpet the banquet room is .

C) Describe how you can estimate the cost to carpet the room.

Page 4: Example 1 – Area of a Composite Figure · D) Describe another way to divide the shape into simpler figures. E) If you divide the composite figure into different shapes, what is

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?


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