What does math have to do with home decorating? Most home decorators need to work within a budget. But in order to figure out what you'll spend, you first have to know what you need. How will you know how many rolls of wallpaper to buy if you don't calculate how much wall space you have to cover? Understanding some basic geometry can help you stick to your budget.

The word geometry literally means "to measure the Earth." Geometry is the branch of math that is concerned with studying area, distance, volume, and other properties of shapes and lines. If you need to know the distance between two points, the volume of water in a pool, the angle of a tennis serve, or how much wallpaper it will take to cover a wall, geometry holds the answers.

Figuring area: Squares and rectangles

Imagine you're planning to buy new carpeting for your home. You're going to put down carpeting in the living room, bedroom, and hallway, but not in the bathroom. You could try to guess at how much carpet you might need to cover these rooms, but you're better off figuring out exactly what you need. To determine how much carpet you'll need, you'll use this simple formula:

A = L x W

Or in other words, "area equals length times width." This formula is used to determine the area of a rectangle or square. In the floor plan below, all of the floor space (as well as the walls and ceilings) is made up of squares or rectangles, so this formula will work for figuring the area you need to carpet.

Start by figuring the total area of the floor plan. When you're done, you can deduct the area of the bathroom, since you don't want to carpet that room. To figure out the total area of the floor plan, you'll need to know the total length and width. The total length of the floor plan shown above is 12 feet plus 10 feet, or 22 feet. The total width is 7 feet plus 5 feet, or 12 feet. Plug these numbers into your equation to get the total area of the floor plan:

A = 22 feet x 12 feet

A = 264 square feet

The total area of your floor plan is 264 square feet. Now you need to figure out the area of the bathroom so you can deduct it from the total area. The bathroom is 7 feet long and 5 feet wide, so it has an area of 35 square feet. Deducting the area of the bathroom from the total area (264 minus 35) leaves you with 229 square feet to carpet.

Figuring area: Circles

Calculating how much carpet you'll need is a fairly simple task if your home has only square or rectangular rooms. But what if you have a circular alcove at the end of one room? How do you figure the area of a circle? Geometry comes to the rescue again with a handy formula:

A = (pi) x r2

In English, this formula means "area equals pi times the radius squared." A circle's radius is one half of its diameter, or one half of what you get if you measure all the way across its widest part. "Squaring" something means you multiply it by itself. Pi is a number that roughly equals 3.14159.

If your living room has a semi-circular alcove as shown in the floor plan above, you'll need to use this additional equation to figure out its area. To figure the radius of your alcove, the number you'll need to plug into the equation, you'll divide its diameter in half. Its diameter is the same as the width of the living room: 12 feet. Half of that is its radius: 6 feet.

Let's plug in the numbers:

A = 3.14159 x (6 feet x 6 feet)

A = 113 square feet (rounded to the closest square foot)

If your alcove were a complete circle, it would have an area of 113 square feet. Because it's a half circle, its area is half of that, or 56.5 square feet. Adding 56.5 square feet to the rest of your floor plan's area of 229 square feet gives you the total area you want to carpet: 285.5 square feet. Using geometry, you can buy exactly the amount of carpet you need.