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Splash Screen. Five-Minute Check (over Lesson 12–3) Main Idea and Vocabulary Key Concept: Surface Area of a Rectangular Prism Example 1: Find Surface Area Example 2: Find Surface Area Example 3: Real-World Example Example 4: Use the Pythagorean Theorem. Lesson Menu.

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  1. Splash Screen

  2. Five-Minute Check (over Lesson 12–3) Main Idea and Vocabulary Key Concept: Surface Area of a Rectangular Prism Example 1: Find Surface Area Example 2: Find Surface Area Example 3: Real-World Example Example 4: Use the Pythagorean Theorem Lesson Menu

  3. Find the surface areas of rectangular prisms. • surface area Main Idea/Vocabulary

  4. KC

  5. Find Surface Area Find the surface area of the rectangular prism. You can use a net of the rectangular prism to find its surface area. There are three pairs of congruent faces. • top and bottom • front and back • two sides Example 1

  6. Find Surface Area Faces Area top and bottom 2(6 ● 2) = 24 front and back 2(6 ● 3) = 36 two sides 2(2 ● 3) = 12 sum of the areas 24 + 36 + 12 = 72 Answer: The surface area is 72 square centimeters. Example 1

  7. A B C D Find the surface area of the rectangular prism. A. 16 ft2 B. 108 ft2 C. 150 ft2 D. 162 ft2 Example 1

  8. Find Surface Area Find the surface area of the rectangular prism. Replace ℓ with 10, w with 8, and h with 12. surface area = 2ℓw+ 2ℓh + 2wh = 2 ●10 ● 8+ 2 ● 10 ● 12 + 2 ● 8 ● 12 = 160 + 240 + 192 Multiply first. Then add. = 592 Answer: 592 in2 Example 2

  9. A B C D Find the surface area of the rectangular prism. A. 22 cm2 B. 210 cm2 C. 254 cm2 D. 312 cm2 Example 2

  10. BOXES Drew is putting together a cardboard box that is 9 inches long, 6 inches wide, and 8 inches high. He bought a roll of wrapping paper that is 1 foot wide and 3 feet long. Did he buy enough to wrap the box? Justify your answer. Step 1 Find the surface area of the box. Replace ℓ with 9, w with 6, and h with 8. surface area = 2ℓw + 2ℓh + 2wh = 2 ● 9 ● 6 + 2 ● 9 ● 8 + 2 ● 6 ● 8 = 348 in2 Example 3

  11. 1 ft 3 ft area = 12 in. ● 36 in. or 432 in2 Step 2 Find the area of the wrapping paper. Answer: Since 348 in2< 432 in2, Drew bought enough paper. Example 3

  12. A B C D A. yes; 360 > 310 B. yes; 328 > 295 C. no; 360 < 412 D. no; 310 < 360 Example 3

  13. Use the Pythagorean Theorem Find the surface area of the rectangular prism. The width and length of the prism are given. To find surface area, you need to find the height of the prism. Notice that the diagonal, length, and height of the front face of the prism form a right triangle. Example 4

  14. Definition of square root Use the Pythagorean Theorem c2 = a2 + b2 Pythagorean Theorem 72 = 32 + b2 Replace c with 7 and a with 3. 49 = 9 + b2 Evalute powers. 49 – 9 = 9 + b2– 9Subtract 9 from each side. 40 = b2 Simplify. ±6.3 = b Simplify. The height of the prism is 6.3 meters. Find the surface area. Example 4

  15. Use the Pythagorean Theorem surface area = 2ℓw + 2ℓh + 2wh = 2 • 3 • 5 + 2 • 3 • 6.3 + 2 • 5 • 6.3 = 30 + 37.8 + 63 Multiply first. Then add. = 130.8 Answer: The surface area of the prism is 130.8 square meters. Example 4

  16. A B C D Find the surface area of a rectangular prism that has width 5 feet, diagonal 13 feet, and height 2 feet. A. 188 square feet B. 215 square feet C. 241 square feet D. 256 square feet Example 4

  17. End of the Lesson End of the Lesson

  18. Five-Minute Check (over Lesson 12–3) Image Bank Math Tools The Pythagorean Theorem Resources

  19. A B C D Solve the problem by making a model. A. B. C. D. (over Lesson 12-3) Five Minute Check 1

  20. A B C D (over Lesson 12-3) Solve the problem by making a model.A sports collector shop arranges four of its most expensive baseball cards in the top display case four in a row. In how many different ways can four baseball cards be arranged in a row? A. 16 B. 12 C. 20 D. 24 Five Minute Check 2

  21. A B C D (over Lesson 12-3) Solve the problem by making a model.Helen wrote checks for $26.75, $134, and $52. If she now has $82.50 in her checking account, how much did she have to begin with? A. $130.25 B. $563 C. $295.25 D. $212.75 Five Minute Check 3

  22. A B C D (over Lesson 12-3) Mr. Green has a square flowerbed that is 8 feet long on each side. He puts a stone border around it that is 1 foot wide. What is the perimeter of the stone border? A. 81 ft B. 64 ft C. 40 ft D. 34 ft Five Minute Check 4

  23. End of Custom Shows

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