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You did these with your group. Now do them on your own — the model above is yours to copy.

1. 1

   Same stepsFinish what the group started. Use the model above, step for step.

   Try it together — then prove it: Now a rectangular prism: 5 long, 4 wide, 3 tall. How many faces does it have? Top and bottom: 5 × 4 = 20, times 2 = 40. Front and back: 5 × 3 = 15, times 2 = 30. Left and right: 4 × 3 = 12, times 2 = 24. Now add 40 + 30 + 24. What is the surface area? Yes, SA = 94 cm². Surface area always uses square units. Now prove it: say why that move had to work at all — not just that it did.

   Show your work
2. 2

   Warm restartSurface area is measured in which type of unit?

   1. ASquare units (in², cm², ft²)
   2. BCubic units (in³, cm³, ft³)
   3. CLinear units (in, cm, ft)
   4. DNo units are needed

   How do you know?
3. 3

   Warm restartHow many faces does a rectangular prism have?

   1. A6
   2. B4
   3. C8
   4. D12

   How do you know?
4. 4

   Warm restartA net of a rectangular prism shows six rectangles with areas 12, 12, 18, 18, 24 and 24 square inches. What is the surface area?

   1. A108 in²
   2. B54 in²
   3. C108 in³
   4. D72 in²

   How do you know?

You answered these out loud. Now write them.

Answer, then say how you know — the reason is the part that counts.

1. 5

   Think it throughWhat is the chest's surface area?

   1. A32 ft²
   2. B24 ft²
   3. C12 ft²
   4. D16 ft²

   Why is that the answer?
2. 6

   Think it throughHow many cans of stain are needed for one chest?

   1. A1
   2. B2
   3. C3
   4. D0

   How do you know? Give a second reason as well.
3. 7

   Think it throughThe carpenter builds a second identical chest. Now how many cans?

   1. A1
   2. B2
   3. C3
   4. D4

   Explain your thinking. What would have to change for a different choice to be right?
4. 8

   Back to the modelCompare Capsule A (rectangular, SA = 248 in²) and Capsule C (triangular, SA = 184 in²). Even though they are similar in size, why does the rectangular prism need more paint?

Use the words

Fill each blank with a word from the bank.

• The total area of a prism's faces, found with SA = 2B + lateral area, is the ___.
• The total area of all the faces of a solid is its ___.
• A solid with six rectangular faces is a ___.
• A solid with two triangular faces and three rectangular faces is a ___.

Explain the thinking

1. 9

   Find the mistakeAnother student made this exact mistake in this lesson. Explain why it is wrong, then write what they should have done.

   The mistake: A common mistake in Surface Area of Prisms is confusing surface area with volume — multiplying l × w × h (which finds the space INSIDE the prism, in cubic units) instead of adding the areas of all the faces (SA = 2lw + 2lh + 2wh, in square units).
2. 10

   Say moreFor the triangular prism (base 6, height 4, length 10, slant sides 5), how did you account for the triangular bases AND the rectangular lateral faces?
3. 11

   Write your ownWrite your own problem about this situation, then solve it and show the answer. The situation: James is putting a restorative stain on the entire outside of the wooden chest. One can of stain covers about 50 square feet.

   Show your work

Last check

These two come from Lesson 5.6. If they are shaky, that is the lesson to revisit — not this one.

1. 12

   Show what you knowExplain your thinking — A rectangular prism has l = 8 ft, w = 6 ft, h = 3 ft. What is the surface area?

   1. A180 ft²
   2. B144 ft²
   3. C180 ft³
   4. D90 ft²

   Explain your choice.
2. 13

   From Lesson 5.6Explain your thinking — A rectangular prism has l = 9 in, w = 5 in, h = 3 in. What is the surface area?

   1. A174 in²
   2. B135 in²
   3. C174 in³
   4. D87 in²

   How do you know?
3. 14

   From Lesson 5.6How many sheets of wrapping paper do you need?

   1. A1
   2. B2
   3. C3
   4. D568

   How do you know?

Be honest — this tells your teacher what to do next