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: A square pyramid has a base that is 4 in by 4 in. Its slant height is 5 in. Find its surface area. Find the base area and the area of the 4 faces. (4 × 4 = 16 and 4 × 10 = 40) What is the surface area? (16 + 40 = 56 square inches) Why must we add the base area? (Surface area covers every face. The square bottom is a face too. Without it, the answer is too small.)

   Show your work
2. 2

   Warm restartHow many faces does a triangular prism have?

   1. A3
   2. B4
   3. C5
   4. D6

   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. A31 cm²
   2. B52 cm²
   3. C62 cm²
   4. D62 cm³

   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. A3 ft²
   2. B6 ft²
   3. C7 ft²
   4. D12 ft²

   Why is that the answer?
2. 6

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

   1. A12 ft²
   2. B24 ft²
   3. C30 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$72
   2. B$144
   3. C$288
   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.

• 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 ___.
• The polygon on the bottom of a pyramid is the ___.

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. A36 in²
   2. B60 in²
   3. C96 in²
   4. D96 in³

   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. A90 ft²
   2. B144 ft²
   3. C180 ft²
   4. D180 ft³

   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