9-3. Area of Irregular Figures Going Deeper EXPLORE. Essential question: How do you find the area of composite figures? Area of a Composite Figure

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1 Name Class Date Area of Irregular Figures Going Deeper Essential question: How do you find the area of composite figures? CC.7.G.6 EXPLORE Area of a Composite Figure video tutor Aaron 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? REFLECT 1. Use dotted lines to show two different ways Aaron s garden could be divided up into simple geometric figures. Chapter Lesson 3

2 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. Shape triangle square rectangle parallelogram trapezoid Area Formula 2 bh s 2 lw bh 2 h( b 1 + b 2 ) 2 CC.7.G.6 EXAMPLE Finding the Area of a Composite Figure Find the area of the figure. A Into what two figures can you divide this composite figure? 3 cm 4 cm 10 cm 2 cm 7 cm B Find the area of each shape. Area of the Parallelogram Area of the Trapezoid 10 cm 3 cm 4 cm The base of the parallelogram is The height of the parallelogram is Use the formula. bh cm. cm. The area of the parallelogram is cm 2. 7 cm The bottom base of the trapezoid is cm. 2 cm The top base the trapezoid is cm, since it is the same length as the base of the parallelogram. The height of the trapezoid is cm. Use the formula. 2 h( b 1 + b 2 ) 2 ( + ) 2 ( ) The area of the trapezoid is cm 2. Chapter Lesson 3

3 C Find the area of the composite figure. + = Area of parallelogram Area of trapezoid Area of composite shape REFLECT 2a. Describe another way to divide the shape into simpler figures. 2b. If you divide the composite figure into different shapes, what is the area? What does this tell you? 3 CC.7.G.6 example Calculating Cost Based on Area A banquet room is being carpeted. A floor plan of the room is shown at right. Each unit length represents 1 yard. Carpet costs $23.50 per square yard. How much will it cost to carpet the room? A Divide the figure into simpler shapes: a parallelogram, a rectangle, and a triangle. Show the divisions on the floor plan with dotted lines. Count the units to find the dimensions. B Find the area of the parallelogram. bh square yards D Find the area of the triangle. 2 bh 2 square yard E The area of the composite figure is yd 2. C Find the area of the rectangle. lw square yards F To calculate the cost to carpet the room, multiply by the. The cost to carpet the banquet room is. Chapter Lesson 3

4 REFLECT 3. Describe how you can estimate the cost to carpet the room. practice Find the area of each figure. Use 3.14 for π cm 5 cm 4 cm 6 m 6 cm 6 cm 4. Show two different ways to divide the composite figure. Find the area both ways. Show your work below. 12 cm 9 cm 5. Sal is tiling 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 tile his entryway? 9 cm 8 cm 20 cm 18 cm 6. Reasoning A composite figure is formed by combining a square and a triangle. Its total area is 32.5 ft 2. The area of the triangle is 7.5 ft 2. What is the length of each side of the square? Chapter Lesson 3

5 Name Class Date 9-3 Additional Practice Estimate the area of each figure. Each square represents 1 square foot. Choose the letter for the best answer A 10 ft 2 C 14 ft 2 B 11 ft 2 D 15 ft 2 F 24 ft 2 H 32 ft 2 G 27 ft 2 J 36 ft 2 Find the area of each figure. Use 3.14 for The figure shows the dimensions of a room. How much carpet is needed to cover the floor? Chapter Practice and Problem Solving

6 Problem Solving Write the correct answer. 1. Explain how to find the area of the composite figure below. Then find the area. 2. Mr. Bemis carpets the living room shown below. If he pays $20 per square meter, what is the total cost of the carpet? 3. A figure is made of a square and a semi-circle. The square has sides of 16 cm each. One side of the square is also the diameter of the semi-circle. What is the total area of the figure? Use 3.14 for. 4. A figure is made of a rectangle and an isosceles right triangle. The rectangle has sides of 6 in. and 3 in. One of the short sides of the rectangle is also one of the legs of the right triangle. What is the total area of the figure? Choose the letter of the correct answer. 5. Norene builds the deck at the right. The area of the deck is 10 m 2 greater than was originally planned. What is the area of the deck? A 110 m 2 C 66 m 2 B 76 m 2 D 56 m 2 6. The grid to the right shows a swimming pool. Each square represents 1 square meter. What is the best estimate of the area of the swimming pool? F 45 m 2 H 37 m 2 G 41 m 2 J 32 m 2 Chapter Practice and Problem Solving