6.3. Surface Area of Solids The Gift Box. My Notes ACTIVITY

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1 Surface Area of Solids SUGGESTED LEARNING STRATEGIES: Activating Prior Knowledge J.T. is the creative director for a paper products company. The company is introducing a new line of gift boxes, called No Wrapping Required, for hard-to-wrap gifts. The boxes come in a variety of shapes, sizes, colors, and themes for birthdays, anniversaries, and holidays. 1. Match each of the following gift boxes with the net used to create it. Give the most appropriate geometric name for each gift box. ACADEMIC VOCABULARY ACTIVITY 6.3 A solid is a three-dimensional figure having length, width, and height. Gift Boxes Nets 4 m 6 m 2 m 6.3 in. 7 in. 5 in. 1 in. 7 in. 4 yd 5 yd 5 yd 10 yd 2 yd Unit 6 Three-Dimensional Geometry 317

2 ACTIVITY 6.3 Surface Area of Solids MATH TERMS The lateral face of a prism is any face that is not the base of the prism. The word lateral means related to the side. SUGGESTED LEARNING STRATEGIES: Interactive Word Wall, Identify a Subtask A lateral face of a solid is a face that is not a base. A right prism is a prism in which the lateral faces are rectangles and are perpendicular to the bases. 2. Examine the right hexagonal prism below. 5 km a. Give the dimensions of each lateral face in the solid, and then find the area of each lateral face. Show your work. b. The lateral area of a solid is the sum of the areas of the lateral faces. Find the lateral area of the solid. Show all your work. 318 SpringBoard Mathematics with Meaning TM Level 3

3 Surface Area of Solids ACTIVITY 6.3 SUGGESTED LEARNING STRATEGIES: Create Representations, Think/Pair/Share, Group Presentation 3. Use the right triangular prism below to complete parts (a) (f). 2 ft 3 ft 4 ft Area of a Triangle: A = 2 1 bh where b represents the length of the base of the triangle and h represents the height of the triangle. a. Sketch each base and label its dimensions. b. Sketch each lateral face and label its dimensions. c. Find the lateral area, L, of the prism. Show all calculations. d. Find the perimeter of the base, P. e. Multiply the perimeter of the base, P, times the height of the prism, h. f. Compare your responses to parts (c) and (e). What do you notice? Unit 6 Three-Dimensional Geometry 319

4 ACTIVITY 6.3 Surface Area of Solids SUGGESTED LEARNING STRATEGIES: Create Representations, Look for a Pattern, Group Presentation, Quickwrite 4. Complete the table below using what you know about prisms. Prism Lateral Area Labeled Sketch of Base Perimeter of Base Height of Prism 4 m 2 m 6 m 5 in. 4 yd 5 yd 5 yd 10 yd 2 yd Area of a Trapezoid: A = 1 2 h ( b 1 + b 2 ), where b 1 and b 2 are the lengths of the bases of a trapezoid and h is the height of the trapezoid. 5. Use variables P, h, and L to explain how to find the lateral area, L, of a prism. 320 SpringBoard Mathematics with Meaning TM Level 3

5 Surface Area of Solids ACTIVITY 6.3 SUGGESTED LEARNING STRATEGIES: Identify a Subtask, Visualization, Quickwrite 6. Find the lateral area, L, for each of the following solids. a. 9 in. 3 in. 3 in. 3 in. b. 5 in. 6 in. 6 in. 9 in. 2 in. c. a rectangular prism with height 10 mm and a square base with side length 4 mm 7. The surface area of a prism is the sum of the areas of the lateral faces and the areas of the bases. Describe the relationship between the lateral area and the surface area of a prism. WRITING MATH Surface area is represented by SA or by T in an expression. Unit 6 Three-Dimensional Geometry 321

6 ACTIVITY 6.3 Surface Area of Solids SUGGESTED LEARNING STRATEGIES: Identify a Subtask, Think/Pair/Share, Group Presentation 8. Consider these gift boxes from the first page of this activity. 1 m 2 = 10,000 cm 2 4 m 2 m 4 yd 5 yd 5 yd 1 yd 2 = 9 ft 2 1 ft 2 = m 10 yd 3 yd 2 yd a. Find the surface area of each box. Show all your calculations. b. Sometimes, you may need to express a measurement in different units from the ones given. Express the surface area of the above-left box in square centimeters. c. What is the surface area of the above-right box in square feet? 9. Find the surface area for each of the following solids. CONNECT TO AP There are many applications of surface area and volume in calculus. a. 12 cm b. A right triangular prism has a height 6 cm. The base of the triangular base is 3 cm and the height of the triangular base is 4 cm. c. Express the surface area you found in 9b in square meters. 322 SpringBoard Mathematics with Meaning TM Level 3