Geometry 10-3 Complete Lesson: Areas of Regular Polygons

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 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.

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.

Vocabulary Review: Which figure is NOT a regular polygon?

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

Reflection: Math Success