Geometry 10-7 Complete Lesson: Areas of Circles and Sectors

By Matt Richardson

Last updated about 3 years ago

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! Each of the regular polygons in the table above has radius 1. Use a calculator to complete the copy of the table on the canvas for the perimeter and area of each polygon. Write out the first 5 decimal places

Solve It! Look at the results in your table. Notice the perimeter and area of an n-gon as n gets very large. Now consider a circle with radius 1. What are the circumference and area of the circle? Explain.

Problem 1 Got It? What is the area of a circular wrestling region with a 42-ft diameter? Round to the nearest square foot. Enter your response in this format: "2810 square feet"

Problem 1 Got It? Reasoning: If the radius of a circle is halved, how does its area change?

Problem 2 Got It?

Problem 3 Got It?

Reasoning: Suppose a sector of ⊙P has the same area as a sector of ⊙O. Can you conclude that ⊙P and ⊙O have the same area? Explain.

Error Analysis: Your class must find the area of a sector of a circle determined by a 150° arc. The radius of the circle is 6 cm. Your classmate performed the steps shown. What is his error? Explain.

Review Lesson 10-6: Find the length of arc AB. Leave your answer in terms of π. Write your response in this form: "14 pi cm"

Review Lesson 10-6: Find the length of arc AB. Leave your answer in terms of π. Write your response in this form: "14 pi m"

Review Lesson 10-6: Find the length of arc AB. Leave your answer in terms of π. Write your response in this form: "14 pi in."

Review Lesson 6-6: Three sides of a trapezoid are congruent. The fourth side is 4 in. longer than each of the other three. The perimeter is 48 in. What are the lengths of the sides? Select all that apply.

9 in.
11 in.
13 in.
15 in.
18 in.

Length of three congruent sides
Length of longest side

Review Lesson 10-7: ⊙A has radius 4 cm, and ⊙B has radius 6 cm. What is the ratio of the area of ⊙A to the area of ⊙B? Write your answer in simplest form. Use this format: "5/13"

Review Lesson 10-7: A large square has side length 24 in. A small square has side length 16 in. What is the ratio of the area of the small square to the large square? Write your answer in simplest form. Use this format "5 : 13"

Vocabulary Review: What is the formula for the area of a parallelogram?

Vocabulary Review: Enter only a number to fill in the blank.

Use Your Vocabulary: Classify the figures the shaded sector from the diagram. Classifications may contain more than one figure. Not all figures will be classified.

CA
AB
sector ABC
CB
sector ACB

arc
radius
shaded sector name

Geometry 10-7 Complete Lesson: Areas of Circles and Sectors

Solve It! Each of the regular polygons in the table above has radius 1. Use a calculator to complete the copy of the table on the canvas for the perimeter and area of each polygon. Write out the first 5 decimal places

Solve It! Look at the results in your table. Notice the perimeter and area of an n-gon as n gets very large. Now consider a circle with radius 1. What are the circumference and area of the circle? Explain.

Problem 1 Got It? What is the area of a circular wrestling region with a 42-ft diameter? Round to the nearest square foot. Enter your response in this format: "2810 square feet"

Problem 1 Got It? Reasoning: If the radius of a circle is halved, how does its area change?

Problem 2 Got It?

Problem 3 Got It?

Reasoning: Suppose a sector of ⊙P has the same area as a sector of ⊙O. Can you conclude that ⊙P and ⊙O have the same area? Explain.

Error Analysis: Your class must find the area of a sector of a circle determined by a 150° arc. The radius of the circle is 6 cm. Your classmate performed the steps shown. What is his error? Explain.

Review Lesson 10-6: Find the length of arc AB. Leave your answer in terms of π. Write your response in this form: "14 pi cm"

Review Lesson 10-6: Find the length of arc AB. Leave your answer in terms of π. Write your response in this form: "14 pi m"

Review Lesson 10-6: Find the length of arc AB. Leave your answer in terms of π. Write your response in this form: "14 pi in."

Review Lesson 6-6: Three sides of a trapezoid are congruent. The fourth side is 4 in. longer than each of the other three. The perimeter is 48 in. What are the lengths of the sides? Select all that apply.

Review Lesson 10-7: ⊙A has radius 4 cm, and ⊙B has radius 6 cm. What is the ratio of the area of ⊙A to the area of ⊙B? Write your answer in simplest form. Use this format: "5/13"

Review Lesson 10-7: A large square has side length 24 in. A small square has side length 16 in. What is the ratio of the area of the small square to the large square? Write your answer in simplest form. Use this format "5 : 13"

Vocabulary Review: What is the formula for the area of a parallelogram?

Vocabulary Review: Enter only a number to fill in the blank.

Vocabulary Review: Enter only a number to fill in the blank.

Vocabulary Review: Enter only a number to fill in the blank.

Use Your Vocabulary: Classify the figures the shaded sector from the diagram. Classifications may contain more than one figure. Not all figures will be classified.

Reflection: Math Success