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.

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.