The formula for the area of a square is . However, the problem gives us a diagonal and not a side.

Remember that all sides of a square are equal, so the diagonal cuts the square into two equal triangles, each a  right triangle.

If we use the Pythagorean Theorem, we see: 

Plug in our given diagonal to solve.

From here we can plug our answer back into our original equation:

If the area of the half circle is , then the area of a full circle is twice that, or .

Use the formula for the area of a circle to solve for the radius:

36π = πr²

r = 6

If the radius is 6, then the diameter is 12. We know that the sides of the square are the same length as the diameter, so each side has length 12.

Therefore the area of the square is 12 x 12 = 144.

The area of a square is equal to its length times its width, so we need to figure out how long each side of the parking lot is. Since a square has four sides we calculate each side by dividing its perimeter by four.

Each side of the square lot will use 40 feet of fence.

^.

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.

The area of the given square is given by so the side must be 6 in.  The side is reduced by a factor of two, so the new side is 3 in.  The perimeter of the new square is given by .

By finding the square root of the area of the garden, you find the length of one side, which is 8. We add 3 feet to this, giving us 11, then multiply this by 4 to get 44 feet for the perimeter.

The area of the shaded region, which covers half of the square is 18 meaning that the total area of the square is 18 x 2, or 36. The area of a square is equal to the length of one side squared. Since the square root of 36 is 6, the length of 1 side is 6. The perimeter is the length of 1 side times 4 or 6 x 4.

The area of a square is given by  so we know the side is 5 cm.  Enlarging by a factor of two makes the new side 10 cm.  The perimeter is given by , so the perimeter of the new square is 40 cm.

In order to find the perimeter of a square, one must add up all of its side lengths. The side lengths of a square are all equal; therefore, the formula for the perimeter of a square is .

Remember perimeter should be expressed in single units not units squared. Thus,  is an incorrect answer.