NAME DATE PERIOD. Plan What will you need to do to solve the problem? Write your plan in steps.

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1 Lesson Multi-Step Example Multi-Step Problem Solving Li is designing a flower bed for a school project. His design consists of a square inside a parallelogram. The shaded area will be planted with small shrubs. In order to get the correct number of shrubs, Li needs to determine the area of the shaded region once he has the dimensions. Which of the following formulas can be used to find the area of the shaded region?.g., MP A A = b h - s C A = b w + s B A = b w - s D A = b h + s h s b w Chapter 9 Use a problem-solving model to solve this problem. Analze Read the problem. Circle the information ou know. Underline what the problem is asking ou to find. Plan What will ou need to do to solve the problem? Write our plan in steps. Step Step Determine the formula for the area of the parallelogram and square. Subtract the area of the square from the area of the parallelogram. Solve Use our plan to solve the problem. Show our steps. Area of Parallelogram - Area of Square = Area of Shaded Region b h - s = b h - s The formula is A = b h - s, so choice Justif and Evaluate How do ou know our solution is accurate? is correct. Fill in that answer choice. Course Chapter 9 Area

2 Lesson (continued) Use a problem-solving model to solve each problem. Beth is creating a flag for an art project. The flag is rectangular with two parallelograms of the same dimensions as seen in the diagram. Which formula can be used to find the area of the shaded region?.g., MP h l The side of an office building is made of mirrored glass panels in the shape of parallelograms. If one parallelogram-shaped piece of glass has a base of. feet and a height of feet, determine how man windows there are in an 0 square foot area..g., MP x w A A = l w - h B A = l w - x h C A = l w - x h D A = l w - h An area of square feet is used for identical parking spaces as seen in the diagram below. Use the information in the diagram to find the height of one parallelogram-shaped parking space, h..g., MP h 0. ft H.O.T. Problem A rectangle is drawn with dimensions units long and units wide. Then a triangle is cut from the rectangle with dimensions shown, and placed on the left side of the rectangle to form a parallelogram..g., MP 7 What are the area and perimeter of the original rectangle? What are the area and perimeter of the parallelogram formed b cutting and moving the triangle? Course Chapter 9 Area

3 Lesson Multi-Step Example Multi-Step Problem Solving The triangle on the grid represents a triangular-shaped pillow. What is the area of the triangle?.g., MP A 70 in B in Chapter 9 C in D in in. Use a problem-solving model to solve this problem. Analze Read the problem. Circle the information ou know. Underline what the problem is asking ou to find. Plan What will ou need to do to solve the problem? Write our plan in steps. Step Step Determine the height of the triangle. Use the formula A = _ bh to find the area of the triangle. Solve Use our plan to solve the problem. Show our steps. Each square on the grid represents or inches. The height of the triangle is or inches. The area of the triangle is bh or. The area is Choice square inches. is correct. Fill in that answer choice. Justif and Evaluate How do ou know our solution is accurate? Course Chapter 9 Area 7

4 Lesson (continued) Use a problem-solving model to solve each problem. The figure below represents a swimming pool. A rope is attached from point A to C, and triangle ABC will be a designated adult swimming area. What is the area of the adult swimming region?.g., MP The triangle on the grid outlines the border of a town. Each square on the grid represents a side length of. miles. What is the area of the town in square miles?.g., MP A 7 ft B ft D C A ft B ft C 9 ft D 7 ft The table shows the dimensions of three triangles. How much greater is the area of triangle C than triangle A, in square centimeters?.g., MP 7 Triangle Base Height A. cm cm B 7 cm 7 cm C 9 cm. cm H.O.T. Problem Marco is going to paint 0% of the triangle. How man square inches will he paint?.g., MP d in. 0 in. Course Chapter 9 Area

5 Lesson Multi-Step Example Multi-Step Problem Solving The figure on the grid represents a parking lot. Asphalt for the parking lot costs $.9 per square foot. How much will it cost to asphalt the parking lot, to the nearest cent?.g., MP Chapter 9 A $90. C $,.00 B $0.0 D $7,.00 ft Use a problem-solving model to solve this problem. Analze Read the problem. Circle the information ou know. Underline what the problem is asking ou to find. Plan What will ou need to do to solve the problem? Write our plan in steps. Step Step Determine the area of the trapezoid. Multipl to determine the cost of the asphalt. Solve Use our plan to solve the problem. Show our steps. Each square on the grid represents a length of or feet. The two bases are feet and 7 feet. The height is 0 feet. A = _ h(b + b ) Area of a trapezoid A = _ (0)(7 + ) Replace h with 0, b with 7, and b with. A =,00 Multipl. So, the cost of the asphalt is $.9,00 or $,. Choice Fill in that answer choice. Justif and Evaluate How do ou know our solution is reasonable? is correct. Course Chapter 9 Area 9

6 Lesson (continued) Use a problem-solving model to solve each problem. The figure on the grid represents the floor of an office. Each square on the grid represents units. Which expression represents an area of a floor that is twice this size?.g., MP A farmer spread fertilizer onto the plot of land shown below. He uses scoops of fertilizer per square meter. If he used scoops, what is the height of the trapezoid in meters?.g., MP m m A _ (7)( + ) B 7( + ) C _ ()( + 0) D ()( + 0) In the figure below, the area inside ABEF will be colored red. What will be the red area, in square feet?.g., MP A in. B 0 in. C in. in. F 0 in. E in. D H.O.T. Problem Suppose the bases and height of a trapezoid are all multiplied b. How will the area change?.g., MP 7 0 Course Chapter 9 Area

7 Lesson Multi-Step Example Multi-Step Problem Solving The side lengths of the smaller triangle are multiplied b the same number to create a larger triangle with a base of foot and height of _ foot. How man times greater is the area of the larger triangle?.g., MP A C 9 B D in. in. Chapter 9 Use a problem-solving model to solve this problem. Analze Read the problem. Circle the information ou know. Underline what the problem is asking ou to find. Plan What will ou need to do to solve the problem? Write our plan in steps. Step Determine the of the smaller triangle. Step Convert the dimensions of the larger triangle to, determine the area, then compare the. Solve Use our plan to solve the problem. Show our steps. Determine the area of the smaller triangle. _ = Determine the area of the larger triangle in inches. ft = = ft = The area of the larger triangle is So, the correct answer is = times larger.. Fill in that answer choice. Justif and Evaluate How do ou know our solution is accurate? Course Chapter 9 Area

8 Lesson (continued) Use a problem-solving model to solve each problem. The side lengths of the rectangle below are multiplied b _. What effect would this have on the perimeter?.g., MP The dimensions of the rectangles listed in the table will all be multiplied b. What is the combined area of the enlarged rectangles in meters?.g., MP ft ft A The perimeter will be _ times greater. B The perimeter will be _ times greater. C The perimeter will be _ times greater. D The perimeter will be times greater. Rectangle Length (cm) Width (cm) Rectangle A Rectangle B Rectangle C 7 9 The Pentagon in Washington, D.C. is a regular pentagon. Juan made two scale models of the Pentagon. The perimeter of the larger model is how man times greater than the perimeter of the smaller model? (Hint: inch. cm).g., MP in. 0. cm H.O.T. Problem The area of Rectangle B is times greater than the area of Rectangle A. Give possible dimensions for each rectangle. Justif our answer..g., MP Course Chapter 9 Area

9 Lesson Multi-Step Example Multi-Step Problem Solving Madeline drew this diagram of her rectangular vegetable garden. What are the coordinates of the vertices of the rectangle she drew? If the length of each grid square on the diagram is ards, what is the area of Madeline s garden?.g., MP 7 O A D B C 7 x Chapter 9 Use a problem-solving model to solve this problem. Analze Read the problem. Circle the information ou know. Underline what the problem is asking ou to find. Plan What will ou need to do to solve the problem? Write our plan in steps. Step Write the coordinates of the vertices of the rectangle e and then determine the length of each side. Step Step Multipl the length and the width of the rectangle b ards to find the length and the width of the garden. Multipl the length b the width to find the area of the garden. Solve Use our plan to solve the problem. Show our steps. The coordinates of the vertices are A(, ), B(, ), C(, ), D(, ). Length: Subtract x-coordinates AB : 7 - = and CD : Width: Subtract -coordinates AD : - = and BC : Multipl the length and the width b ards: =. = Find the area:. The area of the garden is square ards. Justif and Evaluate How do ou know our solution is accurate? Course Chapter 9 Area

10 Lesson (continued) Use a problem-solving model to solve each problem. Hudson drew this diagram of the triangular pen he wants to build for his pet rabbits. What are the coordinates of the vertices of the triangle he drew? If the length of each grid square on the diagram is. feet, what is the area of the pen?.g., MP 7 O C A B 7 x Montrel drew a diagram of his rectangular pool. What are the coordinates of the vertices of the pool he drew? The length of each grid square on the diagram is foot. Montrel wants to put a deck around the outside of his pool that is feet wide on all sides. What will be the perimeter of the outside of the deck?.g., MP 7 O A B D C 7 x The diagram shows the shape and size of two different tiles that Charl wants to use to cover a wall. He wants to cover 7 square feet with each kind of tile. If the length of each grid square on the diagram is foot, how man of each tile does Charl need?.g., MP 7 O Tile A Tile B 7 x H.O.T. Problem Vivian drew two diagrams for flower gardens. The length of each grid square on the diagrams is feet. Vivian wants a flower garden that is square feet. Which diagram should she use for her garden? Explain..G., MP 7 O 7 x 7 O 7 x Course Chapter 9 Area

11 Lesson Multi-Step Example Multi-Step Problem Solving The diagram shows a wall in Javier s living room that he wants to paint. Find the total area to be painted..g., MP A square feet B 9 square feet C 07 square feet D square feet ft ft ft ft ft ft ft ft ft Chapter 9 Use a problem-solving model to solve this problem. Analze Read the problem. Circle the information ou know. Underline what the problem is asking ou to find. Plan What will ou need to do to solve the problem? Write our plan in steps. Step Step Step Find the area of the wall including the windows. Find the areas of the three windows. Subtract the areas of the windows from the total area of the wall. Solve Use our plan to solve the problem. Show our steps. = The area of the wall including the windows is square feet. Window on the left _ = + + = The total area of the windows is square feet. - = The total area to be painted is square feet. So, Middle window = ; _ ()() = + = is the correct answer. Fill in that answer choice. Justif and Evaluate How do ou know our solution is accurate? Window on the right _ = Course Chapter 9 Area

12 Lesson (continued) Use a problem-solving model to solve each problem. The diagram shows where Jada plans to plant flowers and vegetables and place sod in her rectangular backard. How man square meters of sod does she need?.g., MP. m 7 m There are doors into the closet from both Ella s bedroom and Bethan s bedroom. How man square ards of carpet will it take to cover the floors in the two bedrooms and the closet?.g., MP m Vegetables m ft Sod m ft Ella s Room 9 ft 9 ft. m Flowers 7 m ft 9 ft Closet Bethan s Room ft A. square meters B 07. square meters C 9. square meters D 7. square meters ft Eller drew a diagram of a pen she fenced in for her rabbits. What is the area of the pen?.g., MP ft ft 7 ft ft ft ft ft H.O.T. Problem To find the area of the shaded composite figure below, ou can find the sum of the areas of the two shaded triangles and the shaded square. Describe another wa ou can find the area of the shaded composite figure. Then use one of the was to find the area..g., MP in. in. in. in. in. in. in. in. in. Course Chapter 9 Area