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.

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Presentation transcript:

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. SOLUTION STEP 1 Sketch the prism. Imagine unfolding it to make a net.

EXAMPLE 1 STEP 2 Use the net of a prism Find the areas of the rectangles that form the faces of the prism. 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 cm 2.

EXAMPLE 2 Find the surface area of a right prism SOLUTION STEP 1 Find the perimeter and area of a base of the prism. Perimeter P = 5(7.05) Apothem a = √ 6 2 – EXAMPLE 2 Find the surface area of the right pentagonal prism. Find the surface area of a right prism Each base is a regular pentagon. ≈ 4.86 = 35.25

EXAMPLE 2 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. Find the surface area of a right prism The surface area of the right pentagonal prism is about square feet. ANSWER

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

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. for Examples 1 and 2 GUIDED PRACTICE ANSWER (a) NET: Left and right faces: 7 4 = 28 in. 2 Top and bottom faces: 3 4 = 12 in. 2 Front and back faces: 3 7 = 21 in. 2 S = 2(28) + 2(12) + 2(21) = 122 in.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. for Examples 1 and 2 GUIDED PRACTICE ANSWER (b) S = 2B + Ph = 122 in. 2 = 2(3 4)