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**Warm Up 1.) Find the area of the hexagon.**

2.) If a solid has 5 faces, 8 edges, how many vertices does it have? 3.) Sketch a pentagonal pyramid.

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Surface Area of Prisms 12.2

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**Vocabulary Lateral Face – face that is not the base**

Surface Area – the sum of the area of the faces. Net – two-dimensional representation of the faces

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**Formula’s Surface area of a Right Prism S = 2B + Ph = aP + Ph**

Where a is the apothem of the base, B is the area of the base, P is the perimeter of the base, and h is the height of the prism.

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EXAMPLE 1 Use the net of a prism Find the surface area of a rectangular prism with height 2 centimeters, length 5 centimeters, and width 6 centimeters. STEP 1 SOLUTION Sketch the prism. Imagine unfolding it to make a net.

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EXAMPLE 1 Use the net of a prism Find the areas of the rectangles that form the faces of the prism. STEP 2 STEP 3 Add the areas of all the faces to find the surface area. The surface area of the prism is S = 2(12) + 2(10) + 2(30) = 104 cm2.

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**Find the surface area of a right prism**

EXAMPLE 2 EXAMPLE 2 Find the surface area of a right prism Find the surface area of the right pentagonal prism. SOLUTION STEP 1 Find the perimeter and area of a base of the prism. Each base is a regular pentagon. Perimeter P = 5(7.05) = 35.25 Apothem a = √ 62 –3.5252 ≈ 4.86

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**Find the surface area of a right prism**

EXAMPLE 2 Find the surface area of a right prism STEP 2 Use the formula for the surface area that uses the apothem. S = aP + Ph Surface area of a right prism ≈ (4.86)(35.25) + (35.25)(9) Substitute known values. ≈ Simplify. The surface area of the right pentagonal prism is about square feet. ANSWER

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GUIDED PRACTICE for Examples 1 and 2 1. Draw a net of a triangular prism. SOLUTION

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GUIDED PRACTICE for Examples 1 and 2 2. Find the surface area of a right rectangular prism with height 7 inches, length 3 inches, and width 4 inches using (a) a net and (b) the formula for the surface area of a right prism. ANSWER (a) NET: Left and right faces: = 28 in.2 Top and bottom faces: = 12 in.2 Front and back faces: = 21 in.2 S = 2(28) + 2(12) + 2(21) = 122 in.2

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GUIDED PRACTICE for Examples 1 and 2 2. Find the surface area of a right rectangular prism with height 7 inches, length 3 inches, and width 4 inches using (a) a net and (b) the formula for the surface area of a right prism. ANSWER (b) S = 2B + Ph = 2(3 4) = 122 in.2

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Class work 1.)The diagonal of a cube is 8 units, what is the surface area of this cube?

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1.) Total surface area? 2.) 3 in a row removed? 3.) Other 3 removed?

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Homework Page ,5,6,7,8,13,15,23

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