Question

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

Answer 1

Compare the area and perimeter formulas for circles and squares.

Answer 2

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.

Answer 3

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.