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High School Algebra II: Homework Help Resource26 chapters | 280 lessons | 1 flashcard set

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A lot of the conversions we do in our daily lives deal with single measures. But what happens when we must work with square measures? This lesson will focus on just that! Specifically, converting between square feet and square yards.

Say you are remodeling your home and one of the DIY projects on your to-do list is to replace the carpet in your living room with wood floors. After looking back at the floor plan of your home, you know that your living room is 288 square feet. However, all of the flooring you want to buy is measured in yards...What do you do?

I guess you could go through and re-measure you living room using a yardstick but that just seems like unnecessary work. What if I told you, that there is a simple conversion that you can use based off of the standard feet to yards conversion? Sounds a lot easier than re-measuring your entire living room, right?

Before we begin, we should probably do a quick review of our units.

Our basic feet and yards measure the length of an object while square feet and square yards measure its area. If we were measuring in cubic feet, or cubic yards, we would be working with volume.

One of the most common conversions in measurement is the relationship between feet and yards. From a young age, it has been drilled into our heads that there are three feet in one yard. We can use this basic conversion to help us figure out the number of square feet in a square yard.

3 feet = 1 yard

Now, we want to convert this to square feet and square yards so that we can buy the correct amount of flooring for our living room.

If you remember back to your understanding of exponents, square feet is the same as saying, feet^2. When we see an exponent, in this case, 2, it is telling us to multiply that unit by itself twice. This would result in (feet x feet). The same holds true for yards.

In order to convert our singular feet and yards to square feet and yards, we must also square the number associated with each unit. Looking at our basic conversion:

3 feet = 1 yard

(3^2) feet^2 = (1^2) yard^2

9 feet^2 = 1 yard^2

**9 square feet = 1 square yard**

**square feet / 9 = square yards**

Now, we can use the conversion that there are nine square feet in one square yard to figure out the amount of flooring we need for our living room. We can do this by simply dividing our 288 square feet by the nine-foot conversion to get a measure of 32 square yards.

This means that we need 32 square yards of flooring to cover our 288 square foot room.

Say you have a 567 square foot backyard that needs to be covered in grass. You go to your nearest gardening store and you see that grass is sold in square yard pallets. It is now your job to figure out how many square yards of grass we need to completely fill your backyard. Take a minute to solve this problem and then continue below for the solution.

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We can simply use our square yard to square foot conversion to solve this dilemma without returning home to re-measure the backyard.

We know that there are nine square feet in one square yard, therefore, we can divide your 567 square feet by this conversion of nine to get a total of 63 square yards. We need 63 square yards of grass to fill our 567 square foot back yard.

In this lesson you explored the relationship between square feet and square yards. Because if this relationship, you can now divide any square footage by a conversion factor of nine to get a new measure in square yards.

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High School Algebra II: Homework Help Resource26 chapters | 280 lessons | 1 flashcard set

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