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Private Library
Geometry 10-3 Areas of Regular Polygons
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by Matthew Richardson
| 24 Questions
Note from the author:
A complete formative lesson with embedded slideshow, mini lecture screencasts, checks for understanding, practice items, mixed review, and reflection. I create these assignments to supplement each lesson of Pearson's Common Core Edition Algebra 1, Algebra 2, and Geometry courses. See also mathquest.net and twitter.com/mathquestEDU.
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1
10 pts
Solve It: You want to build a koi pond. For the border, you plan to use 3-ft-long pieces of wood. You have 12 pieces that you can connect together at any angle, including a straight angle. If you wat to maximize the area of the pond, in what shape should you arrange the pieces? Sketch a model of your design on the canvas.
2
10 pts
Solve It! Explain the resoning for your koi pond design from the previous item.
3
10 pts
Vocabulary: Define apothem in your own words.
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4
10 pts
Problem 1 Got It?
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5
10 pts
Problem 2 Got It? What is the area of a regular pentagon with an 8-cm apothem and 11.6-cm sides?
92 cm²
3.6 cm²
232 cm²
186 cm²
6
10 pts
Problem 2 Got It? Reasoning: If the side of a regular polygon is reduced to half its length, how does the perimeter of the polygon change? Explain.
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7
10 pts
Problem 3 Got It?
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8
10 pts
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9
10 pts
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10
10 pts
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11
10 pts
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13
10 pts
Vocabulary: What is the relationship between the side length and the apothem in a square?
14
10 pts
Vocabulary: What is the relationship between the side length and the apothem in a regular hexagon?
15
10 pts
Vocabulary: What is the relationship between the side length and the apothem in an equilateral triangle?
16
10 pts
Error Analysis: Your friend says you can use special right triangles to find the apothem of any regular polygon. What is your friend's error? Explain.
17
10 pts
Review Lesson 10-2: What is the area of a kite with diagonals 8 m and 11.5 m?
Enter your response in this format: 23 square meters
18
10 pts
Vocabulary Review: Classify each statement as true or false.
• True
• False
19
10 pts
Vocabulary Review: Which figure is NOT a regular polygon?

20
10 pts
Use Your Vocabulary: Complete the sentence with the correct word from the list.
• In a regular polygon, the apothem is the perpendicular distance from the center to a(n) __?__.
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21
10 pts
Respond with one word.
22
10 pts
Respond with one word.
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10 pts
Respond with one word.
24
10 pts
Reflection: Math Success