If A Circle And A Square Have Same Perimeter Which Has Larger Area?


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Alishan Samdani Profile
Alishan Samdani answered
For this question you can take a sample circle and a sample square, both with the same perimeter.
Suppose the perimeter is 8. This means the square has each side of 2 units (8/4). For the circle it means it has a radius of;
2 pie r = 8
pie r = 4
Radius = r = 1.273.
Now calculate the areas of both the shapes.
Square = 2 x 2 = 4
Circle = pie r^2 = 3.14(1.273)^2
= 5
Therefore the area of the circle is larger than the area of the square if both have the same perimeters.

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