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 diagonal distance from one corner of her room to the other?

So, we need to find the diagonal 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, to find the diagonal, we can think of an isosceles right triangle, where the two equal sides are 15 ft. This is also a 45/45/90 triangle, which means the side lengths follow the ratio of  . 

This means our answer is    .

We could also find this by using Pythagorean Theorem.

Area of a quadrilateral is found by length times width. In a square, these are the same, so the length of side   is a number that, when multiplied by itself is equal to 169.

In other words, take the square root of 169 to find the length of .

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

where a is the length of any side of the square.  Because a square has 4 equal sides, we can use any side in the formula.  To find the length of any side, we will solve for a.  

Now, we know the perimeter of the square is 36in.  So, we will substitute. 

Therefore, the length of one side of the square is 9in.

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 length of one side of her room?

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.

A square has 4 equal sides.  The formula to find perimeter of a square is:

where a is the length of any side.  Now, to find the length of one side, we will solve for a.

We know the perimeter of the square is 60cm.  So, we can substitute and solve for a.  We get

Therefore, the length of one side of the square is 15cm.

Like any polygon, the perimeter of a trapezoid is the total distance around the outside, i.e.

,

where are the lengths of each side.

Let small base length and big base length. 

The perimeter of a trapezoid is equal to the sum of all of the sides, i.e.

,

where are the lengths of each side. 

Substitute  in the formula for the area of a trapezoid:

You do not need to find the individual bases; their sum, , is . You can substitute  into the formula for the area of a trapezoid:

 square inches.

Note that the fact that one base is  inches longer is not important here.

The area of a trapezoid is given by

,

 where ,  are the lengths of each base and is the altitude (height) of the trapezoid.