A circle with radius 8 has as its circumference \(\displaystyle 2 \pi\) times this, or 

\(\displaystyle 2 \pi \cdot 8 = 16 \pi\).

This is also the perimeter of the square, so the sidelength is one fourth of this, or 

\(\displaystyle \frac{1}{4} \cdot 16 \pi = 4 \pi\).

The area is the square of this, or

\(\displaystyle \left ( 4 \pi \right )^{2} = 16 \pi^{2}\).

The length of the hypotenuse of a right triangle with legs 8 and 12 can be determined using the Pythagorean Theorem:

\(\displaystyle \sqrt{8^{2}+12^{2}} = \sqrt{64+144}= \sqrt{208} = \sqrt{16} \cdot \sqrt{13} = 4\sqrt{13}\)

Since this is also the perimeter of the square, its sidelength is one fourth of this, or

\(\displaystyle \frac{ 4\sqrt{13} }{4} =\sqrt{13}\)

The area of the square is the square of this sidelength, or 

\(\displaystyle \left ( \sqrt{13} \right )^{2}= 13\)

The perimeter of a square, and any shape for that matter, is found by adding up all the exterior sides. Since all sides are equal in a square, we can say: \(\displaystyle P=x + x + x + x=4x\)

where \(\displaystyle x\) represents the length of a side

We can solve for the side length using the information provided:

\(\displaystyle 4x=108\)

\(\displaystyle x=27\)

The area of a square is found by squaring the side length: 

\(\displaystyle A=x^2=27^2=729\)

The length of one side of a square is the perimeter divided by 4:

\(\displaystyle \frac{4 ^{d} }{4} = \frac{4 ^{d} }{4 ^{1}} = 4 ^{d-1}\)

Square this to get the area:

\(\displaystyle ( 4 ^{d-1} )^{2} = 4 ^{(d-1) \cdot 2 } = 4 ^{2d- 2 }\)

The sidelength of a square is the square root of its area - in this case, \(\displaystyle \sqrt{256} = 16\) yards. Its perimeter is therefore four times that, or  \(\displaystyle 16 \times 4 = 64\) yards. Multiply by 36 to convert to inches:

\(\displaystyle 64 \times36 = 2,304\) inches.

Multiply each sidelength by four to get the perimeters - they will be 12, 16, 20, 24, and 28 meters, respectively. The mean will be

\(\displaystyle \left (12+ 16 + 20 + 24 + 28 \right ) \div 5 = 100 \div 5 = 20\) meters

This question is a thinly veiled perimeter of a square question. To find the total amount of fencing needed, use the following formula:

\(\displaystyle P=4*s\)

Where \(\displaystyle P\) is the perimeter of a square, and \(\displaystyle s\) is the length of one side.

\(\displaystyle P=4*15\:meters=60 \:meters\)

In order to find the perimeter \(\displaystyle P\) of a given square with side length \(\displaystyle s\), we use the equation \(\displaystyle P=4s\). Given \(\displaystyle s=7cm\), we can therefore conclude that \(\displaystyle P=4(7cm)=28cm\). 

We are told that the area \(\displaystyle A\) of the square is \(\displaystyle 64\). We know the area of a square is defined as \(\displaystyle A=s^{2}\), where \(\displaystyle s\) is the length of the side of the square. We can therefore deduce that \(\displaystyle 64=s^{2}\) and that \(\displaystyle s=8\). 

In order to find the perimeter \(\displaystyle P\) of a given square with side length \(\displaystyle s\), we use the equation \(\displaystyle P=4s\). Given \(\displaystyle s=8\), we can therefore conclude that \(\displaystyle P=4(8)=32\).

In order to find the perimeter \(\displaystyle P\) of a given square with side length \(\displaystyle s\), we use the equation \(\displaystyle P=4s\). Given \(\displaystyle s=19cm\), we can therefore conclude that \(\displaystyle P=4(19cm)=76cm\).