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Illustrative Math
Grade 7
Let’s find the areas of shapes made up of circles.
Illustrative Math Unit 7.3, Lesson 9 (printable worksheets)
The following diagram shows how to relate the area of a circle and its circumference and find the formula for area of a circle.
The area of this field is about 500,000 m^{2}. What is the field’s area to the nearest square meter? Assume that the side lengths of the square are exactly 800 m.
A. 502,400 m^{2}
B. 502,640 m^{2}
C. 502,655 m^{2}
D. 502,656 m^{2}
E. 502,857 m^{2}
Which figure has a longer perimeter, Figure D or Figure E? How much longer?
Perimeter of figure D = 2π + 6
Perimeter of figure E = 1 1/2 π + 4
Figure D is longer by 1/2 π + 2
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.
The Open Up Resources math curriculum is free to download from the Open Up Resources website and is also available from Illustrative Mathematics.
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