While out walking, you find a strange, square-shaped piece of metal. If the side length of the piece is 26 inches, what is the perimeter of the square?

To find the perimeter of a square, simply multiply the side length by 4. We can do this because perimeter is the distance around the outside of a shape, and squares have 4 equal sides.

To find the perimeter of a square, we will use the following formula:

where a, b, c, and d are the lengths of the sides of the square.

Now, we know the width of the square is 18in. Because it is a square, all sides are equal. Therefore, all sides are 18in.

So, we get

A square has 4 equal sides.

Write the formula for the perimeter of a square.

Substitute the side length.

Evaluate the terms on the right.

The answer is:  

Your new friend has a very small, square-shaped dorm room. She tells you that it is only 225 square feet. Assuming this is true, what is the perimeter of her room?

So, we need to find the perimeter of a square. First, we need to find the side length.

Let's begin with our formula for the area of a square:

where s is our side length and A is our area.

With this formula, we can solve for our side length by plugging in our area and square rooting both sides.

Now, we are close but not quite done. We need to multiply our side length by 4, because a square always has 4 equal sides.

The area decreases by 20% of 20%, which is 4%.

The easiest way to see this is to plug in numbers for the sides of the square.  If we are using percentages, it is easiest to use factors of 10 or 100.  In this case we will say that the square has a side length of 10.

10% of 10 is 1, so 20% is 2.  Now we can just increase one of the sides by 2, and decrease another side by 2.  So our rectangle has dimensions of 12 x 8 instead of 10 x 10.  

The original square had an area of 100, and the new rectangle has an area of 96. So the rectangle is 4 square units smaller, which is 4% smaller than the original square.

To find the area of a quadrilateral, multiply length times width. In a square, since all sides are equal,  is both the length and width.

To find the area of the floor, multiply the length of the room by the width (which is the same forumla used to find the area of a square).  The equation can be written:

Substitute feet for and feet for :

Amy will need of carpet.

The perimeter of the rectangle is

 centimeters.

This is also the perimeter of the square, so divide this by  to get its sidelength:

 centimeters.

The area is the square of this, or  square centimeters.

The areas of the four squares can be calculated by squaring their sidelengths. Add these areas, then divide by 4:

 square inches

Multiply the sidelength by 36 to convert from yards to inches:

Square this to get the area:

 square inches