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**Surface Area 10-7 Warm Up Problem of the Day Lesson Presentation**

Course 1 Warm Up Problem of the Day Lesson Presentation

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**Surface Area 10-7 Warm Up Identify the figure described.**

Course 1 10-7 Surface Area Warm Up Identify the figure described. 1. two parallel congruent faces, with the other faces being parallelograms 2. a polyhedron that has a vertex and a face at opposite ends, with the other faces being triangles prism pyramid

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**Surface Area 10-7 Problem of the Day**

Course 1 10-7 Surface Area Problem of the Day Which figure has the longer side and by how much, a square with an area of 81 ft2 or a square with perimeter of 84 ft? A square with a perimeter of 84 ft; by 12 ft

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Course 1 10-7 Surface Area Learn to find the surface areas of prisms, pyramids, and cylinders.

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**Insert Lesson Title Here**

Course 1 10-7 Surface Area Insert Lesson Title Here Vocabulary surface area net

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Course 1 10-7 Surface Area The surface area of a solid figure is the sum of the areas of its surfaces. To help you see all the surfaces of a solid figure, you can use a net. A net is the pattern made when the surface of a solid figure is layed out flat showing each face of the figure.

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**Additional Example 1A: Finding the Surface Area of a Prism**

Course 1 10-7 Surface Area Additional Example 1A: Finding the Surface Area of a Prism Find the surface area S of the prism. A. 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.

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**Additional Example 1A Continued**

Course 1 10-7 Surface Area 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 = = 188 The surface area is 188 in2.

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**Additional Example 1B: Finding the Surface Area of a Prism**

Course 1 10-7 Surface Area Additional Example 1B: Finding the Surface Area of a Prism Find the surface area S of each prism. B. 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.

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**Additional Example 1B Continued**

Course 1 10-7 Surface Area 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 = = 286 Add the areas of each face. The surface area is 286 cm2.

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**Surface Area 10-7 Try This: Example 1A**

Course 1 10-7 Surface Area Try This: Example 1A Find the surface area S of the prism. A. 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.

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**Surface Area 10-7 Try This: Example 1A A: A = 6 3 = 18 A 3 in.**

Course 1 10-7 Surface Area Try This: 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 = = 234 The surface area is 234 in2.

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**Surface Area 10-7 Try This: Example 1B**

Course 1 10-7 Surface Area Try This: Example 1B Find the surface area S of each prism. B. 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.

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**Try This: Example 1B Continued**

Course 1 10-7 Surface Area Try This: Example 1B Continued top side front 8 cm 10 cm 6 cm Front: 10 8 = 80 80 2 = 160 Top: 6 = 60 60 2 = 120 Side: 6 = 48 48 2 = 96 S = = 376 Add the areas of each face. The surface area is 376 cm2.

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Course 1 10-7 Surface Area The surface area of a pyramid equals the sum of the area of the base and the areas of the triangular faces. To find the surface area of a pyramid, think of its net.

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**Additional Example 2: Finding the Surface Area of a Pyramid**

Course 1 10-7 Surface Area Additional Example 2: Finding the Surface Area of a Pyramid Find the surface area S of the pyramid. S = area of square + 4 (area of triangular face) S = s2 + 4 ( bh) 1 2 __ S = ( 7 8) 1 2 __ Substitute. S = 28 S = S = 161 The surface area is 161 ft2.

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**Surface Area 10-7 Try This: Example 2**

Course 1 10-7 Surface Area Try This: Example 2 Find the surface area S of the pyramid. S = area of square + 4 (area of triangular face) 10 ft 5 ft S = s2 + 4 ( bh) 1 2 __ 5 ft S = ( 5 10) 1 2 __ Substitute. 10 ft S = 25 5 ft S = S = 125 The surface area is 125 ft2.

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Course 1 10-7 Surface Area The surface area of a cylinder equals the sum of the area of its bases and the area of its curved surface. To find the area of the curved surface of a cylinder, multiply its height by the circumference of the base. Helpful Hint

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**Additional Example 3: Finding the Surface Area of a Cylinder**

Course 1 10-7 Surface Area Additional Example 3: Finding the Surface Area of a Cylinder Find the surface area S of the cylinder. Use 3.14 for , and round to the nearest hundredth. ft S = area of lateral surface + 2 (area of each base) S = h (2r) + 2 (r2) Substitute. S = 7 (2 4) + 2 ( 42)

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**Additional Example 3 Continued**

Course 1 10-7 Surface Area Additional Example 3 Continued Find the surface area S of the cylinder. Use 3.14 for , and round to the nearest hundredth. S = 7 8 + 2 16 S 7 8(3.14) + 2 16(3.14) Use 3.14 for . S 7 50.24 S S The surface area is about ft2.

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**Surface Area 10-7 Try This: Example 3**

Course 1 10-7 Surface Area Try This: Example 3 Find the surface area S of the cylinder. Use 3.14 for , and round to the nearest hundredth. 6 ft 9 ft S = area of lateral surface + 2 (area of each base) S = h (2r) + 2 (r2) Substitute. S = 9 (2 6) + 2 ( 62)

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**Try This: Example 3 Continued**

Course 1 10-7 Surface Area Try This: Example 3 Continued Find the surface area S of the cylinder. Use 3.14 for , and round to the nearest hundredth. S = 9 12 + 2 36 S 9 12(3.14) + 2 36(3.14) Use 3.14 for . S 9 S S 565.2 The surface area is about ft2.

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**Insert Lesson Title Here**

Course 1 10-7 Surface Area Insert Lesson Title Here Lesson Quiz Find the surface area of each figure. Use 3.14 for . 1. rectangular prism with base length 6 ft, width 5 ft, and height 7 ft 2. cylinder with radius 3 ft and height 7 ft 3. Find the surface area of the figure shown. 214 ft2 188.4 ft2 208 ft2

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