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Lesson Menu 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

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

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KC

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Example 1 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

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Example 1 Find Surface Area FacesArea top and bottom2(6 ● 2) = 24 Answer: The surface area is 72 square centimeters. sum of the areas 24 + 36 + 12 = 72 front and back2(6 ● 3) = 36 two sides2(2 ● 3) = 12

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1.A 2.B 3.C 4.D Example 1 A.16 ft 2 B.108 ft 2 C.150 ft 2 D.162 ft 2 Find the surface area of the rectangular prism.

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Example 2 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 in 2

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1.A 2.B 3.C 4.D Example 2 A.22 cm 2 B.210 cm 2 C.254 cm 2 D.312 cm 2 Find the surface area of the rectangular prism.

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Example 3 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 1Find the surface area of the box. Replace ℓ with 9, w with 6, and h with 8. surface area = 2 ℓ w + 2 ℓ h + 2wh = 2 ● 9 ● 6 + 2 ● 9 ● 8 + 2 ● 6 ● 8 = 348 in 2

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Example 3 Answer: Since 348 in 2 < 432 in 2, Drew bought enough paper. Step 2Find the area of the wrapping paper. area = 12 in. ● 36 in. or 432 in 2 1 ft3 ft

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1.A 2.B 3.C 4.D Example 3 A.yes; 360 > 310 B.yes; 328 > 295 C.no; 360 < 412 D.no; 310 < 360

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Example 4 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. Use the Pythagorean Theorem

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Example 4 c 2 = a 2 + b 2 Pythagorean Theorem The height of the prism is 6.3 meters. Find the surface area. Use the Pythagorean Theorem 7 2 = 3 2 + b 2 Replace c with 7 and a with 3. 49= 9 + b 2 Evalute powers. 49 – 9= 9 + b 2 – 9Subtract 9 from each side. 40= b 2 Simplify. ±6.3= bSimplify. Definition of square root

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

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1.A 2.B 3.C 4.D Example 4 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

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End of the Lesson

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

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1.A 2.B 3.C 4.D Five Minute Check 1 (over Lesson 12-3) A. B. C. D. Solve the problem by making a model.

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1.A 2.B 3.C 4.D Five Minute Check 2 (over Lesson 12-3) A.16 B.12 C.20 D.24 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?

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1.A 2.B 3.C 4.D Five Minute Check 3 (over Lesson 12-3) A.$130.25 B.$563 C.$295.25 D.$212.75 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?

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1.A 2.B 3.C 4.D Five Minute Check 4 (over Lesson 12-3) A.81 ft B.64 ft C.40 ft D.34 ft 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?

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