Name Class Date. Area Using Tangrams. The area of the small square is 1 square unit. Find the area of each of the other tangram pieces.

Transcription

1 Name Class Date -5 Area of Composite Figures Going Deeper Essential question: How can you find the area of a polygon by breaking it into simpler shapes? CC..G. EXPLORE Area Using Tangrams video tutor The area of the small square is square unit. Find the area of each of the other tangram pieces. A Place one large triangle on top of the other large triangle. What is true about these two triangles? What does this mean about the areas of these two triangles? B What is true about the areas of the two small triangles? C Place the two small triangles on top of the square. Remember that the area of the square is. What is the area of each small triangle? this area on the diagram. D Arrange the square and one of the small triangles as shown. What is the combined area? Now place the parallelogram and the other small triangle on top of the combined square and triangle. What is true about the combined area of the parallelogram and one small triangle? Write The two small triangles have area. Therefore, the area of the parallelogram is the same as the area of the. Write the area of the parallelogram on the diagram. Chapter 5 Lesson 5

2 TRY THIS!. Complete the rest of the diagram by filling in the remaining areas. Explain how you found your answers. 2 CC..G. EXAMPLE Finding the Area of a Polygon A 5 Step Draw a horizontal line segment on the diagram that divides the polygon into two rectangles, one on top of the other. What is the length of this segment? the diagram. Step 2 Find the area of the smaller (top) rectangle. Step Find the area of the larger (bottom) rectangle. The base of the larger rectangle is. The height is - =. Step 4 Add the areas from Steps 2 and to find the total area. REFLECT + = Label this length on 2a. Redraw the original polygon. Divide the polygon into two rectangles in a different way and use these two rectangles to find the area. 2b. Does the way you divide the original polygon affect the final answer? Chapter Lesson 5

3 B 2 Step On the diagram, form a square with a missing piece : Extend the top side of the polygon to the right and extend the right side of the polygon up. What is the side length of this square? The area of the square is =. Step 2 Find the area of the rectangular missing piece. b = - 2 = h = - = Step Subtract the area in Step 2 from the area in Step. - = C 7 Step Draw a horizontal line segment on the diagram that divides the polygon into a rectangle and a triangle. Step 2 Find the area of the rectangle. Step Find the area of the triangle. b = - = h = - = bh = = 2 2 Step 4 Add the areas from Steps 2 and to find the total area. TRY THIS! + = 2c. 9 2d. 4 Chapter 7 Lesson 5

4 practice In Hal s backyard, there is a patio, a walkway, and a garden. ft 5 ft Patio Lawn Walkway Garden ft 9 ft Lawn a. Show how to find the total area of the patio, walkway, and garden by adding areas of rectangles. ft b. Show how to find the total area of the patio, walkway, and garden by subtracting areas of rectangles. Chapter Lesson 5

5 Name Class Date -5 Additional Practice Three paintings are shaped like an -foot square, a 7-foot by 4-foot rectangle, and a triangle with a -foot base and a height of 7 feet. If those paintings are hung together on the outside of a building, how much of the building s wall will they cover altogether?. Two diagonals divide a square carpet into 4 congruent triangles. The base of each triangle is 5 feet and the height is 2.5 feet. What is the area of the entire carpet? Chapter 9 Practice and Problem Solving

6 Problem Solving Write the correct answer.. The shape of Nevada can almost be divided into a perfect rectangle and a perfect triangle. About how many square miles does Nevada cover? 2. The shape of Oklahoma can almost be divided into 2 perfect rectangles and triangle. About how many square miles does Oklahoma cover?. The front side of an apartment building is a rectangle 0 feet tall and 25 feet wide. Bricks cover its surface, except for a door and 0 windows. The door is 7 feet tall and feet wide. Each window is 4 feet tall and 2 feet wide. How many square feet of bricks cover the front side of the building? Circle the letter of the correct answer. 5. A figure is formed by a square and a triangle. Its total area is 2.5 m 2. The area of the triangle is 7.5 m 2. What is the length of each side of the square? A 5 meters C 5 meters B 25 meters D.25 meters 4. Each side of a square garden is 2 meters long. A hedge wall meter wide surrounds the garden. What is the area of the entire garden including the hedge wall? How many square meters of land does the hedge wall cover alone?. A rectangle is formed by two congruent right triangles. The area of each triangle is in 2. If each side of the rectangle is a whole number of inches, which of these could not be its perimeter? F 2 inches H 24 inches G inches J 4 inches Chapter 70 Practice and Problem Solving