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

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Lesson Transcript

Instructor:
*Kimberly Osborn*

At a young age, we learned the basic conversion that there are 12 inches in one foot, but what about square inches and square feet? In this lesson you will explore this conversion and how to apply it to real-world situations.

Say you are watching a home makeover TV show and the host has decided to buy marble for new countertops for the kitchen. After meticulously measuring the old countertops, the host has a total area of 1,152 square inches of countertop to replace. But when he goes to the store, he realizes that the marble is sold in square feet, not inches. Instead of going back home and re-measuring the countertops in feet, the host can use a simple conversion tool to find his square footage without stepping foot (pun intended) outside the store.

There is also a very common conversion factor between inches and feet. You probably remember hearing that there are 12 inches in one foot over and over again as a young child. However, what you probably haven't had a lot of experience with is the conversion factor between square inches and square feet. When we talk of square feet, we're talking about the overall area of something that has been measured; **length multiplied by width** or **length x width**.

Let's look at our basic conversion first and then use our understanding of math to turn it into our square conversion. We know that:

12 inches = 1 foot

When we think back to our learning about exponents, we know that a square means to multiply something by itself two times.

Let's review the basic facts about square conversion of inches to square feet:

- A squared unit, such as inches, feet, or yards, measures a length, width, and area. This is why the squared unit is written like this: 1^2.
- A cubic unit measures a length times a width times a height, or a volume. This means that the number will be multiplied by itself three times. A cubic unit will look like this: 1^3.

Now, since we are working with square units, we have to square each number associated with our basic conversion to keep everything balanced.

**12 inches = 1 foot**

**12 inches^2 = 1 foot^2**

This can be written as the math equation:

(12 x 12) inches^2 = (1 x 1) feet^2

144 inches^2 = 1 foot^2

144 square inches = 1 square foot

Using our introduction example for the home makeover TV show, we can now divide our total 1,152 square inches by a factor of 144 to get our total square footage. After doing the division, the TV host would need a total of 8 square feet of marble to build the new kitchen countertops.

Say you have a piece of rectangular poster board that measures 48 inches by 36 inches. What is the total area of the poster board in square feet? Take a minute to solve this problem and then continue for the solution.

We know the area formula for a rectangle: area = length x width. Using this formula we can then find the total area of the poster board in square inches.

**Area = length x width**

Area of the poster board = 48 x 36

Therefore, the total square area = 1,728 square inches

To get the square footage, we divide 1,728 by 144 square inches. This gives us a total of 12 square feet.

In this lesson you learned about the relationship that exists between square inches and square feet. Knowing that there are 144 square inches in a square foot, you can divide the total amount of square inches of the formula length x width. This will give you the answer in square feet.

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

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