Informal Proof: Area of a Circle vs. Area of Inscribed Polygon

Author:
KatGeog
To find the area of a circle you can use the formula, C=.

Find the area of the circle using the formula.

What is the area of a circle with a radius of 1 cm?

Select all that apply
  • A
  • B
  • C
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What is the area of a circle that has a radius of 10 in?

Select all that apply
  • A
  • B
  • C
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Compare to the area of a regular polygon inscribed in a circle.

In an earlier section, we found the area of a regular polygon. We will use the area of a regular polygon to estimate the area of a circle. On your paper, find the area of a circle that has a radius of 6 cm. Label this value, ACTUAL AREA. Use the slider to change the number of sides in the inscribed polygon. Start with 3 sides, then 4 sides, then 5 sides etc. Compare the area of the n-gon to the actual area of the circle.

Question

Move the slider and compare the actual area of the circle to the area of the polygon. Explain what happens as you increase the number of sides on the polygon.

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Question

Do you think that the area of the inscribed regular n-gon is a good estimate for the area of the circle? Why or why not?

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