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

where l is the length and w is the width of the square.

Now, we know the width of the square is 5in.  Because it is a square, all sides are equal.  Therefore, the length is also 5in.  So, we can substitute.  We get

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

where l is the length and w is the width of the square.

Now, we know the length of the square is 9in.  Because it is a square, all sides are equal.  Therefore, the width is also 9in.  So, we get

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

where l is the length and w is the width of the square.

Now, we know the width of the square is 13in.  Because it is a square, all sides are equal.  Therefore, the length is also 13in.

Knowing this, we can substitute into the formula.  We get

The formula for the area, , of a rectangle when we are given its length, , and width, , is .

To calculate this area, just multiply the two terms.

Figure A has area  square inches.

Figure B has area  square inches, 1 foot being equal to 12 inches.

Figure C has area  square inches.

The figures, arranged from least area to greatest, are A, B, C.

Use the surface area formula, substituting  :

 square inches

The area of a rectangle can be found by multiplying the length by the width.

Since 1 yard = 3 feet, multiply each dimension by 3 to convert from yards to feet:

Use the area formula, substituting :

 square feet

For the sake of simplicity, we will assume that the second square has sidelength 1; Then its perimeter is , and its area is .

The perimeter of the first square is  , and its sidelength is . The area of this square is therefore .

The ratio of the areas is therefore .

From the given information we know that the perimeter of the rectangular basement is 74 feet. We also know that one side of the rectangular basement is 15 feet. This means that the opposite side is also 15 feet long because the equivalent opposite sides rule of rectangles. In order to find the lengths of our other two sides of the rectangle, we need to subtract our two 15 feet sides from the perimeters 74 feet.

.

We know that the last two sides have to add up to 44 feet. Since the rules of rectangles say opposite sides are equivalent, we must take 44 feet and divide by the 2 sides. So 44 divided by 2 is 22 feet, meaning each side must be 22 feet. After adding up all the sides we can confirm that our perimeter is 74 feet. 

Now we know all the sides of the rectangle, we are able to move to the next step, finding the area. We must find the area, because the tiles are square feet. So in order to find the area we must take the length of the rectangle and multiply it to the width. 

Knowing the area of the rectangular basement we also know how many tile are needed to fill the basement for the Jones family. It is exactly 330 square feet tile needed.