Question 141854
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.