If the base paths were half of their original length they would be 45 feet long.

To find the area of this new square, one must multiply 45 times 45.

This equals 2025 square feet.

The answer can be found multiple ways, either by adding the area of the two square infields together,

\(\displaystyle 8100 + 8100 = 16,200\ ft^2\).

Or, by picturing the two infields as a rectangle and finding the are by measuring the length and the width. If the length of one side of an infield is 90 feet then the double infield rectangle will have a length of 180 feet and a width of 90 feet.

Therefore, 

\(\displaystyle 90\times180=16,200\ ft^2\)

Given the length of each side of a square, the area of the square is the square of this length. Therefore, since the square has sidelength 3, its area is 

\(\displaystyle 3^{2} = 3 \times 3 = 9\)

Since a square is a rhombus, its area is equal to half the product of the lengths of its diagonals. Each diagonal has length 1, so the area is equal to

\(\displaystyle A = \frac{1}{2} \cdot 1 \cdot 1 = \frac{1}{2}\).

All four sides of a square have the same length, so the common sidelength is one fourth of the perimeter. The perimeter of the given square is 1, so the length of each side is \(\displaystyle \frac{1}{4}\).

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

\(\displaystyle A =\left ( \frac{1}{4} \right )^{2} = \frac{1^{2} }{4^{2} } = \frac{1}{16}\).

The length of each of the (congruent) sides of a square is one fourth its perimeter, so multiply 64 by \(\displaystyle \frac{1}{4}\) to get this length:

\(\displaystyle 64 \times \frac{1}{4} = 16\).

The area of a square is equal to the square of the length of a side, so square 16 to get the area:

\(\displaystyle 16 ^{2} =16 \times 16 = 256\)

First we need to know that the square root of 16 is 4, because if we work backwards we can see that

\(\displaystyle 4 \times 4= 16\Rightarrow \sqrt{16}=4\)

So next we double 4 to get 8. Now we know that one side of our square is 8in.

The formula for area of a square is one side to the power of two (side times side) because all sides of a square are equal in length. So now we just take 8in and multiply it by itself (8in x 8in) we get an answer of \(\displaystyle 64 in^{2}\).

\(\displaystyle \text{Area}=\text{side}^2\)

\(\displaystyle \text{Area}=8^2=8\times 8=64\)

Notice that our answer is in inches squared since we multiplied together two lengths in inches.

We know that the radius of the circle is also half the length of the side of the square; therefore, we also know that the length of each side of the square is 12 inches.

We need to square this number to find the area of the square.

\(\displaystyle A=s^2\)

\(\displaystyle A=12^2\)

\(\displaystyle A=144\)

To find the perimeter of a square, multiply one of its sides by 4.

\(\displaystyle 6\cdot 4=24\)

We know that \(\displaystyle area=length\cdot width\).

We also know that since \(\displaystyle ABCD\) is a square, all of its sides are of equal length.

To get the measure of any one side of \(\displaystyle ABCD\), take the square root of the area:

\(\displaystyle \sqrt{196}=14\) centimeters

Therefore each side of \(\displaystyle ABCD\) is 14 centimeters long.

To find the perimeter, multiply by 4:

\(\displaystyle 14\times4=56\) centimeters