# Basic Geometry : How to find the length of the side of a square

## Example Questions

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### Example Question #1 : How To Find The Length Of The Side Of A Square

A square has an area of , what is the length of its side?

Explanation:

The sides can be found by taking the square root of the area.

, where = side.

So the length of a side is 6.3 cm.

### Example Question #2 : How To Find The Length Of The Side Of A Square

The perimeter of a square is 16. Find the length of each side of this square.

3

8

12

4

4

4

Explanation:

First, know that all the side lengths of a square are equal. Second, know that the sum of all 4 side lengths gives us the perimeter.  Thus, the square perimeter of 16 is written as

where S is the side length of a square. Solve for this S

So the length of each side of this square is 4.

### Example Question #3 : How To Find The Length Of The Side Of A Square

A playground is enclosed by a square fence. The area of the playground is . The perimeter of the fence is . What is the length of one side of the fence?

Explanation:

We will have two formulas to help us solve this problem, the area and perimeter of a square.

The area of a square is:

,

where length of the square and width of the square.

The perimeter of a square is:

Plugging in our values, we have:

Since all sides of a square have the same value, we can replace all and with (side). Our equations become:

Therefore, .

### Example Question #4 : How To Find The Length Of The Side Of A Square

The area of the square shown below is 36 square inches. What is the length of one of the sides?

Cannot be determined from information given.

Explanation:

The area of any quadrilateral can be determined by multiplying the length of its base by its height.

Since we know the shape here is square, we know that all sides are of equal length. From this we can work backwards by taking the square root of the area to find the length of one side.

The length of one (and each) side of this square is 6 inches.

### Example Question #5 : How To Find The Length Of The Side Of A Square

A square has one side of length , what is the length of the opposite side?

Explanation:

One of the necessary conditions of a square is that all sides be of equal length. Therefore, because we are given the length of one side we know the length of all sides and that includes the length of the opposite side. Since the length of one of the sides is 4 we can conclude that all of the sides are 4, meaning the opposite side has a length of 4.

### Example Question #6 : How To Find The Length Of The Side Of A Square

The perimeter of a square is half its area. What is the length of one side of the square?

Explanation:

We begin by recalling the formulas for the perimeter and area of a square respectively.

Using these formulas and the fact that the perimeter is half the area, we can create an equation.

We can multiply both sides by 2 to eliminate the fraction.

To get one side of the equation equal to zero, we will move everything to the right side.

Next we can factor.

Setting each factor equal to zero provides two potential solutions.

or

However, since a square cannot have a side of length 0, 8 is our only answer.

### Example Question #1 : How To Find The Length Of The Side Of A Square

If the area of the square is 100 square units, what is, in units, the length of one side of the square?

Explanation:

### Example Question #2 : How To Find The Length Of The Side Of A Square

In Square . Evaluate  in terms of .

Explanation:

If diagonal  of Square  is constructed, then  is a 45-45-90 triangle with hypotenuse . By the 45-45-90 Theorem, the sidelength  can be calculated as follows:

.

### Example Question #3 : How To Find The Length Of The Side Of A Square

The circle that circumscribes Square  has circumference 20. To the nearest tenth, evaluate .

Explanation:

The diameter of a circle with circumference 20 is

The diameter of a circle that circumscribes a square is equal to the length of the diagonals of the square.

If diagonal  of Square  is constructed, then  is a 45-45-90 triangle with hypotenuse approximately 6.3662. By the 45-45-90 Theorem, divide this by  to get the sidelength of the square:

### Example Question #4 : How To Find The Length Of The Side Of A Square

Rectangle  has area 90% of that of Square , and  is 80% of . What percent of  is ?

Explanation:

The area of Square  is the square of sidelength , or .

The area of Rectangle  is . Rectangle  has area 90% of that of Square , which is ;   is 80% of , so . We can set up the following equation:

As a percent,  of  is

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