Problem Solving: Area and Surface Area of Composite Figures

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Problem Solving: Area and Surface Area of Composite Figures Office Carpeting: READ: The diagram shows the floor of a building. If wall-to-wall carpeting is installed, how many square feet of carpeting are needed? PLAN: Divide the figure into smaller, familiar polygons. Find and add the areas to find the number of square feet of carpeting needed.

Problem Solving: Area and Surface Area of Composite Figures Office Carpeting: SOLVE: Divide the figure into a parallelogram, a right triangle, and a rectangle. Draw lines to divide the figure. Find the areas. Area of a parallelogram: A = bh;A of Parallelogram: ________________ Area of a triangle: A = ½ bh; A of Triangle: ______________________ Area of Rectangle: A = lw; A of Rectangle: ______________________ ADD to find the TOTAL AREA: ______ + ______ + ______ = _________ft²

Problem Solving: Area and Surface Area of Composite Figures Office Carpeting: CHECK: Solve the problem in a different way.

Problem Solving: Area and Surface Area of Composite Figures Face Painting: READ: Karim took six congruent blocks and glued them together to make the L-shaped solid shown. The blocks are cubes with each edge measuring 3 inches. If Karim paints all the surfaces of this new figure, how many square inches will be painted? PLAN: Find the area of one face of a cube. Determine how many faces of each cube will be painted and multiply the area by that number of faces.

Problem Solving: Area and Surface Area of Composite Figures Face Painting: SOLVE: The face of a cube is a square. Area of one face = s². A = (3)(3) = 9 Shade a diagram of each cube to help you determine which faces will be painted. Cube A: 1 top face and 4 side faces painted; 5 faces total. Cube B: 4 side faces painted; 4 faces total. Cube C: 3 side faces and 1 bottom face painted; 4 faces total. Cube D: 1 top face, 1 bottom face, and 2 side faces painted; 4 faces total. Cube E: 1 top face, 1 bottom face, and 2 side faces painted; 4 faces total. Cube F: 1 top face, 1 bottom face, and 3 side faces painted; 5 faces total. The total number of faces shaded will be: 5 + 4 + 4 + 4 + 4 + 5 = 26. Multiply that number by the area of one face: 9 x 26 = 234 in².

Problem Solving: Area and Surface Area of Composite Figures Face Painting: CHECK: Check that your answer is reasonable. Find the total surface area of one cube and multiply by 6, since there are 6 total cubes. Since not all the faces will be painted, a reasonable answer will be less than the number of square inches you just found.