To solve, simply use the formula for the area of a square. Thus,

Remember that a rhombus that is also a rectangle is a square. Knowing that, the calculation is easy:

The length of a segment with endpoints  and  can be found using the distance formula with , , :

This is the length of one side of the square, so the area is the square of this, or 117.

We want to find the area inside the square that is not taken up by the circle. With that in mind, we can say that the area we're looking for can be expressed by. In other words we are subtracting the area of the circle from the area of the square. This will give us the desired area. 

Now, substitute our known values in for the variables to find the desired area:

The diagonal shown has length 6 meters; to convert to centimeters, multiply by 100: 

The easiest way to find the area of the square given the length of a diagonal is to note that since a square is a rhombus, its area is equal to half the product of the lengths of its diagonals. Since one diagonal has length 600 centimeters, so does the other, and the area of the square is therefore

One meter comprises 100 centimeters, so divide the perimeter of the sides in centimeters by 100 to obtain the length in meters. This is the same as moving the decimal point left two spaces: 

The perimeter of a square is equal to the sum of the lengths of its four equally long sides, so the length of one side is one fourth of - or, in decimal form, 0.25 times - its perimeter. For this square, this is:

The area of a square is equal to the square of the length of one side, so 

The perimeter of a square is equal to the sum of the lengths of its four equally long sides, so the length of one side is one fourth of its perimeter. For this square, this is:

12 inches are equal to one foot, so divide by 12 to convert to feet:

The area of a square is equal to the square of the length of one side, so 

Area of a square in terms of each of its sides:

  Area = S x S

Perimeter of a square:

  Perimeter = 4S

So if 'the perimeter of a square is equal to twice its area':

  2 x Area = Perimeter

  2 x [S x S] = [4S]; divide by 2:

  S x S = 2S; divide by S:

  S = 2

To inscribe means to draw inside a figure so as to touch in as many places as possible without overlapping. The circle is inside the square such that the diameter of the circle is the same as the side of the square, so the side is actually 4 in.  The perimeter of the square = 4s = 4 * 4 = 16 in.

Find the area of Square Y, then calculate the area of Square X.

If the perimeter of Square Y is 24, then each side is 24/4, or 6.

A = 6 * 6 = 36 sq ft, for Square Y

If Square X has 3 times the area, then 3 * 36 = 108 sq ft.