Jeff M.

asked • 05/31/20

A circle is cut into congruent sections and arranged to form a figure that approximates a parallelogram. Find the approximate height of the figure when its area is 72.25π square centimeters.

Mark M.

"approximates as parallelogram" is an ambiguous description. Be more specific.
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05/31/20

Brenda D.

tutor
I agree with Mark above is this approximate parallelogram possibly an approximate Rhombus? Do you have a picture?
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05/31/20

Mark M.

Could it be figure with the four corners forming the four corners of a square?
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05/31/20

Arthur D.

tutor
This is how you derive the area of a circle. Divide the circle into many, many sectors and arrange them one up and the adjacent down and you will see that the figure approaches a parallelogram whose height approximates the radius of the circle and whose base is half of the circle's circumference. A=bh, A=(1/2)(C)(r), A=(1/2)(2*pi*r)(r), A=(1/2)(2)(pi)(r)(r), A=pi*r^2. This is common in middle school and high school math books. I used to be a math teacher and students would always ask why you use A=pi*r^2. So I would always derive the formula before actually writing it. Google this and see what you find !
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05/31/20

1 Expert Answer

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Arthur D. answered • 05/31/20

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the approximate height of the figure is the radius of the circle

A=∏r^2

72.25∏=∏r^2

divide both sides by ∏

72.25=r^2

√72.25=√r^2

8.5=r

r=8.5 cm is the approximate height (or radius)



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Mark M.

What if they were arranged with the 8 radii form the sides of a square?
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05/31/20

Arthur D.

tutor
This is not what the student meant. Arrange the sectors next to each other, one up and one down, and if you divide the circle into smaller and smaller sectors, the figure appears to look like a parallelogram.
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05/31/20

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