name date lesson 7.5 extra practice find the surface area of the rectangular prism. 1 2 3 find the surface area of the triangular prism. 4. 5. 6 7. your friend finds the surface area of the cube. is your friend correct? explain your reasoning. the surface are of the cube is 75 square centimeters. 8. a box is in the shape of a cube with edge lengths of 9 inches. find the surface area of the box. 9. a shipping crate in the shape of a rectangular prism measures 5 feet by 4 feet by 3 feet. find the surface area of the crate. 252 big ideas math: modeling real life grade 6 resources by chapter copyright © big ideas learning, llc all rights reserved.

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### Problem 1: Surface Area of Rectangular Prism (4 cm, 1 cm, 5 cm)
# Explanation:
## Step1: Recall formula for surface area of rectangular prism: $ SA = 2(lw + lh + wh) $
Here, $ l = 4 $ cm, $ w = 1 $ cm, $ h = 5 $ cm.
## Step2: Calculate each term:
$ lw = 4 \times 1 = 4 $, $ lh = 4 \times 5 = 20 $, $ wh = 1 \times 5 = 5 $
## Step3: Substitute into formula:
$ SA = 2(4 + 20 + 5) = 2(29) = 58 $
# Answer: 58 square centimeters

### Problem 2: Surface Area of Rectangular Prism (2 ft, 5 ft, 5 ft)
# Explanation:
## Step1: Use formula $ SA = 2(lw + lh + wh) $
$ l = 2 $ ft, $ w = 5 $ ft, $ h = 5 $ ft.
## Step2: Compute terms:
$ lw = 2 \times 5 = 10 $, $ lh = 2 \times 5 = 10 $, $ wh = 5 \times 5 = 25 $
## Step3: Substitute:
$ SA = 2(10 + 10 + 25) = 2(45) = 90 $
# Answer: 90 square feet

### Problem 3: Surface Area of Rectangular Prism (9 m, 6 m, 2 m)
# Explanation:
## Step1: Apply formula $ SA = 2(lw + lh + wh) $
$ l = 9 $ m, $ w = 6 $ m, $ h = 2 $ m.
## Step2: Calculate each product:
$ lw = 9 \times 6 = 54 $, $ lh = 9 \times 2 = 18 $, $ wh = 6 \times 2 = 12 $
## Step3: Substitute and simplify:
$ SA = 2(54 + 18 + 12) = 2(84) = 168 $
# Answer: 168 square meters

### Problem 4: Surface Area of Triangular Prism (Base: 8 in, 3 in; Sides: 5 in, 4 in, 5 in; Length: 5 in)
# Explanation:
## Step1: Surface area of triangular prism: $ SA = 2B + Ph $ (B: area of triangular base, P: perimeter of base, h: length of prism)
## Step2: Calculate B: $ B = \frac{1}{2} \times 8 \times 3 = 12 $
## Step3: Calculate P: $ 8 + 4 + 5 = 17 $ (Wait, base triangle sides: 8, 4, 5? Wait, the triangle has base 8, height 3, and other sides 5, 4, 5? Wait, 8, 4, 5? Wait, 3-4-5 triangle? Wait, base is 8, height 3, and the two equal sides? Wait, maybe the base triangle is 8, 4, 5? Wait, no, the triangle has base 8, height 3, and the other sides: 5, 4, 5? Wait, perimeter P: 8 + 4 + 5 = 17? Wait, no, the sides of the triangle: 8 in, 4 in, 5 in? Wait, the diagram shows 5 in, 3 in (height), 8 in (base), 4 in, 5 in. So the triangular base has sides 8, 4, 5? Wait, no, 8, 5, 5? Wait, maybe I misread. Wait, the triangle: base 8 in, height 3 in, and the two equal sides are 5 in? Wait, 3-4-5 triangle: if height is 3, base is 8, then the two equal sides would be 5 (since 3-4-5: 4 is half of 8? Wait, no, 8 is the base, so half of 8 is 4, then the side is $ \sqrt{3^2 + 4^2} = 5 $. So the triangle is isoceles with base 8, equal sides 5, height 3. So perimeter P: 8 + 5 + 5 = 18.
## Step4: So $ SA = 2 \times 12 + 18 \times 5 = 24 + 90 = 114 $
# Answer: 114 square inches

### Problem 5: Surface Area of Triangular Prism (Base: 13 in, 5 in, 12 in; Length: 20 in)
# Explanation:
## Step1: $ SA = 2B + Ph $
## Step2: B: $ \frac{1}{2} \times 12 \times 5 = 30 $ (since 5-12-13 is a right triangle)
## Step3: P: $ 5 + 12 + 13 = 30 $
## Step4: $ SA = 2 \times 30 + 30 \times 20 = 60 + 600 = 660 $
# Answer: 660 square inches

### Problem 6: Surface Area of Triangular Prism (Base: 10 cm, 8 cm, 6 cm; Length: 2 cm)
# Explanation:
## Step1: $ SA = 2B + Ph $
## Step2: B: $ \frac{1}{2} \times 6 \times 8 = 24 $ (since 6-8-10 is a right triangle)
## Step3: P: $ 6 + 8 + 10 = 24 $
## Step4: $ SA = 2 \times 24 + 24 \times 2 = 48 + 48 = 96 $
# Answer: 96 square centimeters

### Problem 7: Friend's Cube Surface Area
# Explanation:
## Step1: Surface area of cube: $ SA = 6s^2 $ (6 faces, each $ s^2 $)
## Step2: Friend used $ SA = 3s^2 $ (only 3 faces), which is wrong.
## Step3: Correct calculation: $ 6 \times 5^2 = 6 \times 25 = 150 $
# Brief Explanations: The friend is incorrect. A cube has 6 identical square faces, not 3. The correct formula is $ SA = 6s^2 $. For $ s = 5 $ cm, $ SA = 6 \times 25 = 150 $ square centimeters, not 75.
# Answer: The friend is incorrect. The correct surface area is 150 square centimeters.

### Problem 8: Cube with edge 9 inches
# Explanation:
## Step1: Formula for cube surface area: $ SA = 6s^2 $
## Step2: Substitute $ s = 9 $: $ SA = 6 \times 9^2 = 6 \times 81 = 486 $
# Answer: 486 square inches

### Problem 9: Rectangular Prism (5 ft, 4 ft, 3 ft)
# Explanation:
## Step1: Formula $ SA = 2(lw + lh + wh) $
## Step2: Substitute $ l = 5 $, $ w = 4 $, $ h = 3 $
## Step3: Calculate terms: $ lw = 20 $, $ lh = 15 $, $ wh = 12 $
## Step4: $ SA = 2(20 + 15 + 12) = 2(47) = 94 $
# Answer: 94 square feet

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QUESTION IMAGE

Question

Explanation:

Problem 1: Surface Area of Rectangular Prism (4 cm, 1 cm, 5 cm)

Step1: Recall formula for surface area of rectangular prism: \( SA = 2(lw + lh + wh) \)

Step2: Calculate each term:

Step3: Substitute into formula:

Step1: Use formula \( SA = 2(lw + lh + wh) \)

Step2: Compute terms:

Step3: Substitute:

Step1: Apply formula \( SA = 2(lw + lh + wh) \)

Step2: Calculate each product:

Step3: Substitute and simplify:

Answer:

Problem 2: Surface Area of Rectangular Prism (2 ft, 5 ft, 5 ft)