Start here

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 smaller square pyramid: base 4 × 4, slant height 5. What is the base area? Right, 4 × 4 = 16. Now one triangular face: ½ × 4 × 5. What do you get? Yes, 10. Four faces is 4 × 10 = 40. Now add the base: 16 + 40. What is the surface area? Yes, SA = 56 in². Don't forget to add the base area! Now prove it: say why that move had to work at all — not just that it did.

   Show your work
2. 2

   Warm restartHow many faces does a triangular prism have?

   1. A4
   2. B5
   3. C6
   4. D3

   How do you know?
3. 3

   Warm restartA prism's faces have areas 10 cm², 10 cm², 6 cm², 6 cm², 15 cm² and 15 cm². What is the surface area?

   1. A62 cm²
   2. B31 cm²
   3. C62 cm³
   4. D52 cm²

   How do you know?
4. 4

   Warm restartA triangular prism has two triangular bases each with area 12 cm² and three rectangular faces with areas 30 cm², 40 cm², and 40 cm². What is the total surface area?

   1. A110 cm²
   2. B122 cm²
   3. C134 cm²
   4. D134 cm³

   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 area of one triangular face?

   1. A6 ft²
   2. B12 ft²
   3. C7 ft²
   4. D3 ft²

   Why is that the answer?
2. 6

   Think it throughWhat is the total glass area for all four faces?

   1. A24 ft²
   2. B30 ft²
   3. C12 ft²
   4. D33 ft²

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

   Think it throughWhat will the glass cost?

   1. A$288
   2. B$72
   3. C$144
   4. D$396

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

   Back to the modelDisplay B has the largest surface area (280 in²). What contributes more to the total — the base or the lateral faces? Why?

Use the words

Fill each blank with a word from the bank.

• The total area of a pyramid's faces, found with SA = B + lateral area, is the ___.
• A solid with a polygon base and triangular faces meeting at one point is a ___.
• The height of a triangular face of a pyramid, measured along the slanted side, is the ___.
• A triangular side face of a pyramid 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 Pyramids is finding the four triangular lateral faces correctly (½ × base edge × slant height, times 4) and then stopping — forgetting to add the base area at the end.
2. 10

   Say moreFor Display A (square base 6×6, slant height 8), how did you combine the base area and the four triangular faces to get the total surface area?
3. 11

   Write your ownWrite your own problem about this situation, then solve it and show the answer. The situation: The blueprint shows a right square pyramid with the measurements of its base and its slant height labeled.

   Show your work

Last check

These two come from Lesson 5.7. If they are shaky, that is the lesson to revisit — not this one.

1. 12

   Show what you knowExplain your thinking — A square pyramid has a base edge of 6 in and a slant height of 5 in. What is the total surface area?

   1. A96 in²
   2. B60 in²
   3. C96 in³
   4. D36 in²

   Explain your choice.
2. 13

   From Lesson 5.7Explain 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

   How do you know?
3. 14

   From Lesson 5.7The carpenter builds a second identical chest. Now how many cans?

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

   How do you know?

Be honest — this tells your teacher what to do next