Area is the measure of the amount of surface covered by something. Area formulas for different shapes are sometimes different, but for the most part, area is calculated by multiplying length times width. This is used when calculating area of squares and rectangles. Once you have the number answer to the problem, you need to figure out the units. When calculating area, you will take the units given in the problem (feet, yards, etc) and square them, so your unit measure would be in square feet (ft.2) (or whatever measure they gave you).
Area Example 1
Let’s try an example. Nancy has a vegetable garden that is 6 feet long and 4 feet wide. It looks like this:
Nancy wants to cover the ground with fresh dirt. How many square feet of dirt would she need?
We know that an answer in square feet would require us to calculate the area. In order to calculate the area of a rectangle, we multiply the length times the width. So, we have 6 x 4, which is 24. Therefore, the area (and amount of dirt Nancy would need) is 24 square feet.
Area Example 2
Let’s try that one more time. Zachary has a wall that he would like to paint. The wall is 10 feet wide and 16 feet long. It looks like this:
How many square feet will he be painting?
Using Area and Perimeter Together
Sometimes, you will be given either the area or the perimeter in a problem and you will be asked to calculate the value you are not given. For example, you may be given the perimeter and be asked to calculate area; or, you may be given the area and be asked to calculate the perimeter. Let’s go through a few examples of what this would look like:
Area and Perimeter Example 1
Valery has a large, square room that she wants to have carpeted. She knows that the perimeter of the room is 100 feet, but the carpet company wants to know the area. She knows that she can use the perimeter to calculate the area.
What is the area of her room?
We know that all four sides of a square are equal. Therefore, in order to find the length of each side, we would divide the perimeter by 4. We would do this because we know a square has four sides, and they are each the same length and we want the division to be equal. So, we do our division—100 divided by 4—and get 25 as our answer. 25 is the length of each side of the room. Now, we just have to figure out the area. We know that the area of a square is length times width, and since all sides of a square are the same, we would multiply 25 x 25, which is 625. Thus, she would be carpeting 625 square feet.
Area and Perimeter Example 2
Now let’s see how we would work with area to figure out perimeter. Let’s say that John has a square sandbox with an area of 100 square feet. He wants to put a short fence around his sandbox, but in order to figure out how much fence material he should buy, he needs to know the perimeter. He knows that he can figure out the perimeter by using the area.
What is the perimeter of his sandbox?
We know that the area of a square is length times width. In the case of squares, these two numbers are the same. Therefore, we need to think, what number times itself gives us 100? We know that 10 x 10 = 100, so we know that 10 is the length of one side of the sandbox. Now, we just need to find the perimeter. We know that perimeter is calculated by adding together the lengths of all the sides. Therefore, we have 10 + 10 + 10 + 10 = 40 (or, 10 x 4 = 40), so we know that our perimeter is 40 ft. John would need to buy 40 feet of fencing material to make it all the way around his garden.
Calculating Area and Perimeter Using Algebraic Equations
So far, we have been calculating area and perimeter after having been given the length and the width of a square or rectangle. Sometimes, however, you will be given the total perimeter, and a ratio of one side to the other, and be expected to set up an algebraic equation (using variables) in order to solve the problem. We’ll show you how to set this up so that you can be successful in solving these types of problems.
Eleanor has a room that is not square. The length of the room is five feet more than the width of the room. The total perimeter of the room is 50 ft. Eleanor wants to tile the floor of the room. How many square feet (ft 2) will she be tiling?
