Problem Solving
Solve problems related to the total area of rectangular figures.
Goal:
Goal:
Practice!
Goal: Check your understanding of area and using decomposition to find the total area.
Remember, when you are finding the total area of something, you find the area of each section, then add the different areas together.
An area with the left width 4 inches the top length 8 inches the right width 3 inches and the bottom length 5 inches we can seperate the shapes at the 5 inches mark vertically up and down. now we can find the area. 4 inches times 5 inches equal 20 inches\({^2}\) next 3 inches times 3 inches equals 9 inches\({^2}\) Now we add the 2 areas together 20 inches\({^2}\) plus 9 inches\({^2}\) equal 29 inches\({^2}\)
Let's practice finding the total area of a rectangular figures. Remember to use these problem-solving steps to help you find the answers to word problems.
Word Problem Solving Steps
- Read the problem.
- Look for important information.
- Write a math sentence.
- Choose a way to solve.
- Solve and label your answer.
Solve for the total area using decomposition.
Hector is putting a porch around the side of his house. He needs to find the total area that the porch will cover. What is the area of the porch?
That’s right, Area of left side is 9 feet \({\times}\) 4 feet \({=}\) 36 ft\({^2}\), Area of front is 7 feet \({\times}\) 3 feet \({=}\) 21 ft\({^2}\), Total area of porch is 36 ft\({^2}\) \({+}\) 21 ft\({^2}\) \({=}\) 57 ft\({^2}\)
That’s incorrect. Remember to break the figure into smaller rectangular shapes, then find the area of each section, and finally add the different areas together.
Solve for the total area using decomposition.
Shannon is going to lay some grass in her yard and needs to figure out the area of the space. Use the image below to calculate the total area that will need grass.
That’s right, Area of the yard can be broken into two sections, one is 4 feet \({\times}\) 5 feet \({=}\) 20 ft\({^2}\), and the other is 3 feet \({\times}\) 2 feet \({=}\) 6 ft\({^2}\), Total area of the yard is 20 ft\({^2}\) \({+}\) 6 ft\({^2}\) \({=}\) 26 ft\({^2}\)
That’s incorrect. Remember to break the figure into smaller rectangular shapes, then find the area of each section, and finally add the different areas together.
Solve for the total area using decomposition.
Rhett is going to paint the side of his house. The wall has a height of 15 meters in the front and 10 meters in the back. The roof is 8 meters wide, and the ground level is 12 meters. What is the total area of the wall he is going to paint?
That’s right, Area of the wall can be broken into two sections, one is 12 meters \({\times}\) 10 meters \({=}\) 120 m\({^2}\), and the other is 8 meters \({\times}\) 5 meters \({=}\) 40 m\({^2}\), Total area of the wall is 120 m\({^2}\) \({+}\) 40 m\({^2}\) \({=}\) 160 m\({^2}\)
That’s incorrect. Remember to break the figure into smaller rectangular shapes, then find the area of each section, and finally add the different areas together.
Solve for the total area using decomposition.
Desmond has a corner desk in his bedroom and wants to put a new top on it to match his new style. What is the area of the tabletop he needs to buy?
That’s right, Area of one section is 2 units \({\times}\) 10 units \({=}\) 20 square units, Area of the other section is 9 units \({\times}\) 3 units \({=}\) 27 square units, Total area of the tabletop is 20 square units \({+}\) 27 square units \({=}\) 47 square units.
That’s incorrect. Remember to break the figure into smaller rectangular shapes, then find the area of each section, and finally add the different areas together.
Solve for the total area using decomposition.
Kylie makes a tower with her blocks. If each block is 1 unit high, what is the total area of the tower?
That’s right, Area of the top section is 3 units \({\times}\) 2 units \({=}\) 6 square units, Area of the bottom section is 5 units \({\times}\) 6 units \({=}\) 30 square units, Total area of the tower is 6 square units \({+}\) 30 square units \({=}\) 36 square units
That’s incorrect. Remember to break the figure into smaller rectangular shapes, then find the area of each section, and finally add the different areas together.
Great Job!