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.

   Let's try together: 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!

   My first step is ___ , because the problem asks for ___ .

   Show your work
2. 2

   Warm restartHow many faces does a triangular prism have?

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

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?

   I chose ___ because ___ .
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?

   I chose ___ because ___ .
3. 7

   Think it throughWhat will the glass cost?

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

   Explain your thinking.

   I chose ___ because ___ .
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?

   For Display B, the base area is ___ in² and the total lateral area is 4 × ___ = ___ in². The ___ contribute(s) more because ___.

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?

   The base area is ___ × ___ = ___, and one triangular face is ½ × 6 × 8 = ___.
3. 11

   Change one numberGo back to Part 1 and pick one problem you already solved. Change one number in it, then solve your new version. Show every step.

   If ___ changed to ___ , then ___ .

   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 knowQuick check — you've got this: 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.

   I know it is ___ because ___ .
2. 13

   From Lesson 5.7Quick check — you've got this: 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
3. 14

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

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

Be honest — this tells your teacher what to do next