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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: A regular pentagon splits into 5 equal triangles. Each triangle has a base of 4 cm and a height of 3 cm. The height is rounded, so estimate the area. Find the area of one triangle. Then find the pentagon's area. (1/2 × 4 × 3 = 6, and 5 × 6 = 30 square centimeters) Why does a pentagon split into 5 triangles, not 6? (There is one triangle for each side. A pentagon has 5 sides, so it has 5 triangles.) Why is 30 square centimeters only an estimate? (The height 3 cm was rounded. The real height is a little less, so the real area is a little less.)

   Show your work
2. 2

   Warm restartHow many triangular faces does a square pyramid have?

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

   How do you know?
3. 3

   Warm restartTo find the surface area of a pyramid you add…

   1. Athe area of the base and the areas of all the triangular faces
   2. Bthe volume and the base area
   3. Cthe base perimeter and the height
   4. Donly the triangular faces

   How do you know?
4. 4

   Warm restartA triangular pyramid has a base area of 20 in² and three faces of 14 in² each. What is its surface area?

   1. A34 in²
   2. B54 in²
   3. C62 in²
   4. D62 in³

   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 center triangle?

   1. A7.5 sq ft
   2. B11 sq ft
   3. C15 sq ft
   4. D30 sq ft

   Why is that the answer?
2. 6

   Think it throughWhat is the total floor area of the octagon?

   1. A15 sq ft
   2. B40 sq ft
   3. C120 sq ft
   4. D360 sq ft

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

   Think it throughWhat will the flooring cost?

   1. A$45
   2. B$120
   3. C$360
   4. D$960

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

   Back to the modelThe hexagon and the octagon both have triangles, but the totals are different. What two things decide the total area of a regular polygon?

Use the words

Fill each blank with a word from the bank.

• A polygon with all sides and all angles equal is a ___.
• To break a shape into smaller shapes is to ___ it.
• A three-sided polygon is a ___.
• Made of two or more shapes combined, a figure is ___.

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 Area of Regular Polygons is stopping after finding the area of ONE triangle and reporting that as the total area — or adding the number of triangles instead of multiplying.
2. 10

   Say moreYou matched each regular polygon to its number of center triangles. What pattern connects the number of SIDES to the number of TRIANGLES, and why?
3. 11

   Write your ownWrite your own problem about this situation, then solve it and show the answer. The situation: The firm's blueprint shows a regular pentagon-shaped plaza. Dashed lines run from the center point to each of the 5 corners, dividing the plaza into 5 triangular sections.

   Show your work

Last check

These two come from Lesson 5.8. If they are shaky, that is the lesson to revisit — not this one.

1. 12

   Show what you knowExplain your thinking — A regular pentagon is decomposed into 5 triangles from its center. Each triangle has a base of 7 inches and a height of 4.8 inches. What is the total area of the pentagon?

   1. A16.8 sq in
   2. B84 sq in
   3. C84 in
   4. D168 sq in

   Explain your choice.
2. 13

   From Lesson 5.8Explain 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

   How do you know?
3. 14

   From Lesson 5.8What will the glass cost?

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

   How do you know?

Be honest — this tells your teacher what to do next