The formula for the area, \(\displaystyle A\), of a rectangle when we are given its length, \(\displaystyle L\), and width, \(\displaystyle W\), is \(\displaystyle A = L * W\).

To calculate this area, just multiply the two terms.

\(\displaystyle A = 14\ cm * 12\ cm = 168\; cm^{2}\)

Figure A has area \(\displaystyle 10 \times 14 = 140\) square inches.

Figure B has area \(\displaystyle 12 \times 12 = 144\) square inches, 1 foot being equal to 12 inches.

Figure C has area \(\displaystyle \frac{1}{2} \times 16 \times 20 = 160\) square inches.

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

Use the surface area formula, substituting \(\displaystyle L = 22, W = H = 12\) :

\(\displaystyle A = 2LW + 2LH + 2WH\)

\(\displaystyle A = 2 \cdot 22 \cdot 12 + 2 \cdot 22 \cdot 12 + 2\cdot 12\cdot 12\)

\(\displaystyle A = 528 + 528 + 288\)

\(\displaystyle A =1,344\) square inches

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

\(\displaystyle A=l\times w\)

\(\displaystyle 48=3x\times x=3x^2\)

\(\displaystyle 48=3x^2\)

\(\displaystyle \frac{48}{3}=\frac{3x^2}{3}\)

\(\displaystyle 16=x^2\)

\(\displaystyle \sqrt{16}=\sqrt{x^2}\)

\(\displaystyle 4=x\)

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

\(\displaystyle 8 \textrm{ yd} \times 3 \textrm{ ft/yd} = 24 \textrm{ ft}\)

\(\displaystyle 3 \textrm{ yd} \times 3 \textrm{ ft/yd} = 9 \textrm{ ft}\)

Use the area formula, substituting \(\displaystyle L = 24, W = 9\):

\(\displaystyle A = LW\)

\(\displaystyle A = 24 \times 9 = 216\) square feet

For the sake of simplicity, we will assume that the second square has sidelength 1; Then its perimeter is \(\displaystyle 4 \times 1 = 4\), and its area is \(\displaystyle 1^{2} = 1\).

The perimeter of the first square is \(\displaystyle \frac{7}{4} \times 4 = 7\) , and its sidelength is \(\displaystyle 7 \div 4 = \frac{7}{4}\). The area of this square is therefore \(\displaystyle \left (\frac{7}{4} \right )^{2} =\frac{49}{16}\).

The ratio of the areas is therefore \(\displaystyle \frac{49}{16} : 1 = 49:16\).

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.

\(\displaystyle 74-30=44\ feet\).

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. 

\(\displaystyle 22\times 15= 330 ft^{2}\)

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.

Divide each dimension by 100 to convert centimeters to meters:

\(\displaystyle 250 \div 100 = 2.5\)

\(\displaystyle 140 \div 100 = 1.4\)

Multiply length by width:

\(\displaystyle 2.5 \times 1.4 = 3.5\) square meters

Multiply length times width to get the area in square meters:

\(\displaystyle A = 1,400 \times 800 = 1,120,000\) square meters

Divide by 10,000 to convert to hectares:

\(\displaystyle 1,120,000 \div 10,000 = 112\) hectares

Divide each dimension by 12 to convert from inches to feet:

\(\displaystyle 27 \div 12 = 2.25\)

\(\displaystyle 15 \div 12 = 1.25\)

Multiply length by width:

\(\displaystyle 2.25 \times 1.25 = 2.8125\) square feet