Question 141854This question is from textbook Prentice Hall Mathmatics Pre-Algrebra
: Thanks for helping me in advance. I can`t seem to find the answer to this question. Here is the question:
You have three pieces of string, each 60 cm long. You form a circle with one piece, a square with another, and an equilateral triangle with the third piece. How do the areas of the three figures compare? Explain.
Thanks again in advance for helping!
This question is from textbook Prentice Hall Mathmatics Pre-Algrebra
Found 2 solutions by stanbon, scott8148:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! You have three pieces of string, each 60 cm long. You form a circle with one piece, a square with another, and an equilateral triangle with the third piece. How do the areas of the three figures compare? Explain.
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The circle has a circumference of 60 cm
Find the radius so you can find its area.
2(pi)r = 60
r = 30/pi
Area = (pi)(30/pi)^2 = 900/pi sq cm
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The square has 4 sides that are each 60/4 = 15 cm
Area = 15^2 = 225 sq cm
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The triangle has three sides that are each 20 cm.
base = 20 cm
Draw a perpendicular bisector from the base to the vertex; height = h
h^2 + 10^2 = 20^2
h^2 = 400-100 = 300
h = 10sqrt(3)
Area = (1/2)bh
Area = (1/2)20*10sqrt(3)
Area = 100sqrt(3) sq cm
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Now you can compare the areas any way you want to.
Cheers,
Stan H.
Answer by scott8148(6628)  (Show Source):
You can put this solution on YOUR website! for a fixed perimeter (60 cm), as the number of sides of a regular polygon increases, the enclosed area increases
so the triangle has the least area, the square the 2nd least;
__ and the circle (an infinitely sided polygon) has the most area
the apothem formula for area reflects this __ area=(perimeter)(apothem)/2
__ with the perimeter constant, the apothem (and the area) increases with the number of sides
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