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Geometry 10-3 Complete Lesson: Areas of Regular Polygons

By Matt Richardson
Last updated about 3 years ago
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.

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.

Solve It! Explain the resoning for your koi pond design from the previous item.

Vocabulary: Define apothem in your own words.

Problem 1 Got It?

Problem 2 Got It? What is the area of a regular pentagon with an 8-cm apothem and 11.6-cm sides?

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.

Problem 3 Got It?

Vocabulary: What is the relationship between the side length and the apothem in a square?

Vocabulary: What is the relationship between the side length and the apothem in a regular hexagon?

Vocabulary: What is the relationship between the side length and the apothem in an equilateral triangle?

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.

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

Vocabulary Review: Classify each statement as true or false.

  • In a regular polygon, all sides are congruent.
  • In a regular polygon, all angles are congruent.
  • True
  • False

Vocabulary Review: Which figure is NOT a regular polygon?

Use Your Vocabulary: Complete the sentence with the correct word from the list.

  • angle
  • side
  • In a regular polygon, the apothem is the perpendicular distance from the center to a(n) __?__.

Respond with one word.

Respond with one word.

Respond with one word.

Reflection: Math Success