Lesson 9Applying Area of Circles
Learning Goal
Let’s find the areas of shapes made up of circles.
Learning Targets
I can calculate the area of more complicated shapes that include fractions of circles.
I can write exact answers in terms of
.
Lesson Terms
- area of a circle
- squared
Warm Up: Still Irrigating the Field
Problem 1
The area of this field is about 500,000 m². What is the field’s area to the nearest square meter? Assume that the side lengths of the square are exactly 800 m.
502,400 m
502,640 m
502,655 m
502,656 m
502,857 m
Activity 1: Comparing Areas Made of Circles
Problem 1
Each square has a side length of 12 units. Compare the areas of the shaded regions in the 3 figures. Which figure has the largest shaded region? Explain or show your reasoning.
Problem 2
Each square in Figures D and E has a side length of 1 unit. Compare the area of the two figures. Which figure has more area? How much more? Explain or show your reasoning.
Are you ready for more?
Problem 1
Which figure has a longer perimeter, Figure D or Figure E? How much longer?
Activity 2: The Running Track Revisited
Problem 1
The field inside a running track is made up of a rectangle 84.39 m long and 73 m wide, together with a half-circle at each end. The running lanes are 9.76 m wide all the way around.
What is the area of the running track that goes around the field? Explain or show your reasoning.
Lesson Summary
The relationship between
Sometimes instead of leaving
We can also figure out the area of a fraction of a circle. For example, the figure shows a circle divided into 3 pieces of equal area. The shaded part has an area of