Asked by A
Latoya cut a circle into 8 equal sections and arranged the pieces to form a shape resembling a parallelogram.
C. Since this new shape was made from a circle, use the information from the diagram and the fomula for the area of the parallelogram, A=bh, to discover the formula for the area of a circle.
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GPT-5 mini
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Arrange the 8 equal circular sectors alternately (point up, point down) so the curved edges line up to form a parallelogram-like shape.
- The base of that shape is the sum of the arc lengths of half the sectors, i.e. half the circle’s circumference. So base b = (1/2)(2πr) = πr.
- The height h is the radius r (the distance from the center to the arc).
Using A = b·h:
A = (πr)·r = πr^2.
Thus the area of a circle is A = πr^2.
- The base of that shape is the sum of the arc lengths of half the sectors, i.e. half the circle’s circumference. So base b = (1/2)(2πr) = πr.
- The height h is the radius r (the distance from the center to the arc).
Using A = b·h:
A = (πr)·r = πr^2.
Thus the area of a circle is A = πr^2.
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