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Warm Up

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. Surface Area of Prisms. 12.2. Vocabulary. Lateral Face – face that is not the base Surface Area – the sum of the area of the faces.

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Warm Up

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  1. 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.

  2. Surface Area of Prisms 12.2

  3. 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

  4. 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.

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

  6. 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 cm2. EXAMPLE 1 Use the net of a prism STEP 2

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

  8. ANSWER The surface area of the right pentagonal prism is about 488.57square feet. EXAMPLE 2 Find the surface area of a right prism STEP 2 Use the formula for the surface area that uses the apothem. Surface area of a right prism S = aP + Ph ≈ (4.86)(35.25) + (35.25)(9) Substitute known values. ≈ 488.57 Simplify.

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

  10. 7 4 = 28 in.2 3 4 = 12 in.2 3 7 = 21 in.2 GUIDED PRACTICE for Examples 1 and 2 2. Find the surface area of a right rectangular prism with height 7inches, length 3inches, and width 4inches using (a) a net and (b) the formula for the surface area of a right prism. ANSWER (a) NET: Left and right faces: Top and bottom faces: Front and back faces: S = 2(28) + 2(12) + 2(21) = 122 in.2

  11. 2(3 4) + 14 7 = GUIDED PRACTICE for Examples 1 and 2 2. Find the surface area of a right rectangular prism with height 7inches, length 3inches, and width 4inches using (a) a net and (b) the formula for the surface area of a right prism. ANSWER (b)S = 2B + Ph = 122 in.2

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

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

  14. Homework • Page 806-807 4,5,6,7,8,13,15,23

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