Question 1143631: An octagon, a triangle and a circle all have the same distance around That's perimeter for the octagon and triangle, and circumference for the circle). Which is true of the areas of these shapes. (O=area of octagon, T= area of triangle and c= area of circle)
E) O < C < T
F) O = T = C
G) C > T = C
H) C > O > T
Answer by Edwin McCravy(20056)   (Show Source):
You can put this solution on YOUR website!
The circle is the one figure that has the greatest possible area for a
given perimeter. So we know that the circle has the largest area.
If you had been given that the octagon is a regular octagon and that the
triangle is equilateral, the answer would be
H) C > O > T
However, since this is not given, we can't be sure of that.
For a given perimeter, the area of an n-sided polygon can have any
area between 0 and the area of a n-sided regular polygon with that perimeter.
Since we cannot be sure that the octagon is regular and the triangle is
equilateral, there is no way to know whether the octagon has a greater area
than the triangle, or vice-versa. We can only know that the circle's
area is the largest of the three.
Without knowing whether the octagon is regular and the triangle is
equilateral, we can't solve the problem. The problem is botched
without that information. But the circle has the greatest area.
Edwin
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