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OpenStudy (anonymous):
if a square and a circle have the same perimeter, the circle has a smaller area. state weather it is always true sometimes true or never true
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OpenStudy (anonymous):
Compare the area and perimeter formulas for circles and squares.
OpenStudy (anonymous):
i.e. Perimeter of a square of side length, s, = 4s, and its area is s^2. Perimeter of a circle of radius, r, = 2πr, and its area is πr^2. Try setting those two perimeters equal and figuring out the areas from that.
OpenStudy (fellowroot):
OpenStudy (anonymous):
Or: \[\large 4s=2πr\] \[\large s=\frac{1}{2}πr\] \[\large s^2 = \frac{πr^2}{4}\] Therefore, area of square is one-fourth the area of a circle of equal perimeter.
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