Surface Area Rectangular Prisms Notes Page 46.

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Surface Area Rectangular Prisms Notes Page 46

The surface area of a three- dimensional figure is the sum of the areas of its surfaces. To help you see all the surfaces of a three-dimensional figure, you can use a net. A net is the pattern made when the surface of a three-dimensional figure is layed out flat showing each face of the figure.

Additional Example 1A: Finding the Surface Area of a Prism Find the surface area S of the prism. Method 1: Use a net. Draw a net to help you see each face of the prism. Use the formula A = lw to find the area of each face.

Additional Example 1A Continued A: A = 5  2 = 10 B: A = 12  5 = 60 C: A = 12  2 = 24 D: A = 12  5 = 60 E: A = 12  2 = 24 F: A = 5  2 = 10 Add the areas of each face. S = 10 + 60 + 24 + 60 + 24 + 10 = 188 The surface area is 188 in2.

Additional Example 1B: Finding the Surface Area of a Prism Find the surface area S of each prism. Method 2: Use a three-dimensional drawing. Find the area of the front, top, and side, and multiply each by 2 to include the opposite faces.

Additional Example 1B Continued Front: 9  7 = 63 63  2 = 126 Top: 9  5 = 45 45  2 = 90 Side: 7  5 = 35 35  2 = 70 S = 126 + 90 + 70 = 286 Add the areas of each face. The surface area is 286 cm2.

Check It Out: Example 1A Find the surface area S of the prism. Method 1: Use a net. A 3 in. 3 in. 6 in. 6 in. 3 in. 3 in. 6 in. 11 in. 11 in. B C D E F 3 in. Draw a net to help you see each face of the prism. Use the formula A = lw to find the area of each face.

Check It Out: Example 1A A: A = 6  3 = 18 A 3 in. B: A = 11  6 = 66 3 in. 6 in. 6 in. 3 in. C: A = 11  3 = 33 11 in. D: A = 11  6 = 66 B C D E E: A = 11  3 = 33 F 3 in. F: A = 6  3 = 18 Add the areas of each face. S = 18 + 66 + 33 + 66 + 33 + 18 = 234 The surface area is 234 in2.

Check It Out: Example 1B Find the surface area S of each prism. Method 2: Use a three-dimensional drawing. top side front 8 cm 10 cm 6 cm Find the area of the front, top, and side, and multiply each by 2 to include the opposite faces.

Check It Out: Example 1B Continued top side front 8 cm 10 cm 6 cm Front: 8  6 = 48 48  2 = 96 Top: 10  6 = 60 60  2 = 120 Side: 10  8 = 80 80  2 = 160 S = 160 + 120 + 96 = 376 Add the areas of each face. The surface area is 376 cm2.