Importance of the Math Concept Area

Definition of Area
Area Defined.

 Deb Russell

Area is a mathematical term defined as the two-dimensional space taken up by an object, notes Study.com, adding that the use of area has many practical applications in building, farming, architecture, science, and even how much carpet you'll need to cover the rooms in your house.

Sometimes the area is quite easy to determine. For a square or rectangle, the area is the number of square units inside a figure, says "Brain Quest Grade 4 Workbook," because such polygons have four sides, and you can determine the area by multiplying the length by the width. Finding the area of a circle, however, or even a triangle can be more complicated and involves the use of various formulas. To truly understand the concept of area—and why it's important in business, academics, and everyday life—it's helpful to look at the history of the math concept, as well as why it was invented.

History and Examples

Some of the first known writing about area came from Mesopotamia, says Mark Ryan in "Geometry for Dummies, 2nd Edition." The high school math teacher who also teaches a workshop for parents and has authored numerous math books, says that the Mesopotamians developed the concept to deal with the area of fields and properties:

"Farmers knew that if one farmer planted an area three times as long and twice as wide as another farmer, then the bigger plot would be 3 x 2 or six times as large as the samller one."

The concept of area had many practical applications in the ancient world and in past centuries, Ryan notes:

  • The architects of the pyramids at Giza, which were built about 2,500 B.C., knew how large to make each triangular side of the structures by using the formula for finding the area of a two-dimensional triangle.
  • The Chinese knew how to calculate the area of many different two-dimensional shapes by about 100 B.C.
  • Johannes Keppler, who lived from 1571 to 1630, measured the area of sections of the orbits of the planets as they circled the sun using formulas for calculating the area of an oval or circle.
  • Sir Isaac Newton used the concept of area to develop calculus.

So ancient humans, and even those who lived up through the Age of Reason, had many practical uses for the concept of area. And the concept became even more useful in practical applications once simple formulas were developed to find the area of various two-dimensional shapes.

Formulas to Determine the Area

Before looking at the practical uses for the concept of area, you first need to know formulas for finding the area of various shapes. Fortunately, there are many formulas used to determine the area of polygons, including these most common ones:

Rectangle

A rectangle is a special type of quadrangle where all the interior angles are equal to 90 degrees and all opposite sides are the same length. The formula for finding the area of a rectangle is:

  • A = H x W

where "A" represents the area, "H" is the height, and "W" is the width.

Square

A square is a special type of a rectangle, where all the sides are equal. Because of that, the formula for finding a square is simpler than that for finding a rectangle:

  • A = S x S

where "A" stands for the area and "S" represents the length of one side. You simply multiply two sides to find the area, since all sides of a square are equal. (In more advanced math, the formula would be written as A = S^2, or area equals side squared.)

Triangle

A triangle is a three-sided closed figure. The perpendicular distance from the base to the opposite highest point is called the height (H). So the formula would be:

  • A = ½ x B x H

where "A," as noted, stands for the area, "B" is the base of the triangle, and "H" is the height.

Circle

The area of a circle is the total area that is bounded by the circumference or the distance around the circle. Think of the area of the circle as if you drew the circumference and filled in the area within the circle with paint or crayons. The formula for the area of a circle is:

  • A = π x r^2

In this formula, "A," is, again, the area, "r" represents the radius (half the distances from one side of the circle to the other), and π is a Greek letter pronounced "pi," which is 3.14 (the ratio of a circle’s circumference to its diameter).

Practical Applications

There are many authentic and real-life reasons where you would need to calculate the area of various shapes. For instance, suppose you are looking to sod your lawn; you would need to know the area of your lawn in order to purchase enough sod. Or, you may wish to lay carpet in your living room, halls, and bedrooms. Again, you need to calculate the area to determine how much carpeting to purchase for the various sizes of your rooms. Knowing the formulas to calculate areas will help you determine the areas of the rooms.

For example, if your living room is 14 feet by 18 feet, and you want to find the area so that you can buy the correct amount of carpet, you would use the formula for finding the area of a rectangle, as follows:

  • A = H x W
  • A = 14 feet x 18 feet
  • A = 252 square feet.

So you would need 252 square feet of carpet. If, by contrast, you wanted to lay tiles for your bathroom floor, which is circular, you would measure the distance from one side of the circle to the other—the diameter—and divide by two. Then you would apply the formula for finding the area of the circle as follows:

  • A = π(1/2 x D)^2

where "D" is the diameter, and the other variables are as described previously. If the diameter of your circular floor is 4 feet, you would have:

  • A = π x (1/2 x D)^2
  • A = π x (1/2 x 4 feet)^2
  • A = 3.14 x (2 feet)^2
  • A = 3.14 x 4 feet
  • A = 12.56 square feet

You would then round that figure off to 12.6 square feet or even 13 square feet. So you would need 13 square feet of tile to complete your bathroom floor.

If you have a really original-looking room in the shape of a triangle, and you want to lay carpet in that room, you would use the formula for finding the area of a triangle. You'd first need to measure the base of the triangle. Suppose you find that the base is 10 feet. You'd measure the height of the triangle from the base to the top of the triangle's point. If the height of your triangular room's floor is 8 feet, you'd use the formula as follows:

  • A = ½ x B x H
  • A = ½ x 10 feet x 8 feet
  • A = ½ x 80 feet
  • A = 40 square feet

So, you'd need a whopping 40 square feet of carpet to cover the floor of that room. Make sure you have enough credit remaining on your card before heading to the home-improvement or carpeting store.