From the figure, you should notice that the diameter of the circle is also the diagonal of the square.

In order to find the area of the shaded region, we will first need to find the area of the circle and the area of the square.

First, recall how to find the area of a circle.

Now, use the diameter to find the radius.

Substitute in the given value of the diameter to find the length of the radius.

Simplify.

Now, substitute in the value of the radius into the equation to find the area of the circle.

Simplify.

Now, we will need to find the area of the square.

Notice that the diagonal of the square is also the hypotenuse of a right isosceles triangle that has the sides of the square as the legs of the triangle. We can then use the Pythagorean theorem.

Now, recall how to find the area of a square:

Notice that the area of the square is the same as the equation we found through using the Pythagorean theorem.

So now, we can write the following equation:

Substitute in the value of the diagonal to find the area of the square.

Simplify.

Now, to find the area of the shaded region, subtract the area of the square from the area of the circle.

Solve.

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

If the formula escapes you, draw a picture and imagine you have 2 rows of objects with two in them each. If you add them together, you will get a total of 4!

Because the area of Square A is , and the formula for the area of a square is , we simply plug it in, as follows:

So the length of Square A's sides is . In order to get the length of Square B's sides, we must multiply this by , which gives us .

We then plug this into the formula for area:

To find the area of a square you must know that a square has four sides and all sides are the same length. The formula for finding the area of a square is the length multiplied by the width, or .

The length times width in this case would be .

When answering an area question the answer must be put in units squared, or . In this case it would be inches squared, or .

Therefore the answer is 

To find the area of a square you must know that a square has four sides and all sides are the same length. The formula for finding the area of a square is the length multiplied by the width, or .

The length times width in this case would be .

When answering an area question the answer must be put in units squared, or . In this case it would be inches squared, or .

Therefore the answer is 

The formula for the area of a square is , with  being one side of the square. Since we know one side is , we simply plug this in to get the area, as follows:

.

*Note that while the statement about perimeter is true (and always will be, since the formula for the perimeter of a square is ), this statement is not needed to solve the problem. 

A cube has 6 faces with congruent squares. Since the length of one edge is 5 inches, the area of that face is .

Multiply this by the 6 faces present to get  .

To find the area of the square, use the equation 

or 

.  

For a square, the base and height are the same so to find the area, you can multiply one side by itself.  

In the case of this problem, the base is .  

When we square this value, the area of the square is 

To find the length of one side, we have to work backwards using the formula to find the area of a square.  

That formula is 

.  

Since we know the area is , we can plug that into the equation and solve for .  

Take the square root of  to find .  

This means that our final answer is  and that is the length of one side of the square.

To find the area of the square, use the same formula: 

.  

Although the base is a radical, we can still use this formula.  When we multiply two radicals, we multiply the value under the radical and take the root of that.  In other words, we have to multiply 6 by 6 and take its square root.  

This means we take the square root of 36, which is 6.  Another way, when you multiply two square roots that are the same, the roots cancel and you get the value that is under the radical.  Therefore, the area of the square is .