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Author: Colleen Atakpu

This lesson applies the formulas for area to calculate for unknown values. 

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Today we're going to talk about area. The area of an object is the amount of space that's enclosed within a two dimensional object. So for example, you might find the area of your kitchen floor if you were doing some remodeling. And because area looks at the amount of space within two dimensions, we write our units for area in a little bit different way.

So you might have a unit for length as feet or inches. But because, again, we're looking at two dimensions when we're calculating the area, we write the units for area as feet squared or inches squared. You could also see this sometimes written as sq dot whatever the unit is, so square feet. And similarly for inches, square inches.

So we're going to look at a couple formulas for finding the area for rectangles and circles. And we'll do some examples, calculating the area for each of those shapes. So let's do an example with that area of a rectangle. The formula for the area of a rectangle is the area is equal to the base of the rectangle times the height. So for this example, I've got a base of 15.5 feet and a height of 9 feet. So I can use my formula to find the area.

So substituting my values in, I'll have the area is equal to 15.5 feet multiplied by my height, which is 9 feet. So 15.5 multiplied by 9 is going to give me 139.5, and feet times feet is going to give me feet squared, which matches up with what I know about the units for area.

So for my second example, I've got another rectangle with an area of 75 feet squared and a base of 7.5 feet squared. So now I can use my formula to find the height of my rectangle. Substituting my values in, I've got 75 feet squared is going to be equal to my base, 7.5 feet, times my height. I don't know what that is yet.

So to solve for my height, I'm going to divide by 7.5 feet on both sides. 75 divided by 7.5 just gives me 10. And feet squared divided by feet is going to give me feet. So my height is the height of my rectangle, is 10 feet.

So let's look at the area of a circle. The formula for the area of a circle is pi, which we're going to approximate with 3.14, times my radius of the circle, squared. So for this example, I've got a radius of 8 inches, and I'm going to go ahead and use my formula to find the area of the circle. So the area is going to be equal to pi times my radius, 8 inches, squared. I'm going to start by simplifying my exponent. So 8 inches squared is going to give me 64 inches squared. And I'll bring down the rest of my problem.

Now I'm using my approximation for pi of 3.14. So when I multiply that times 64, I'm going to find that I have an area of approximately 200.96 inches squared for the area of my circle. So for this example, I know the area of my circle is 150 centimeters squared, so I can use my formula to find the radius.

So I'm going to start by substituting the value in for my area, so that will be equal to pi times r squared. So now to solve for r, I'm going to cancel out pi by dividing. And I'll do that on both sides. Since I'm using an approximation for pi-- 3.14, this is going to be equal to approximately 47.77 centimeters squared, which will be equal to my radius squared.

Now to cancel out my 2 exponent, I'm going to take the square root of both sides. And when you take the square root, you actually get a positive and negative answer. But we only need to consider our positive answer, because we're looking at a distance-- the radius of the circle. So the square root of 47.77 is approximately 6.91. My centimeter squared will become centimeters. And that will be equal to my radius.

Now if we wanted to find the diameter of the circle, knowing the radius is 6.91, we could simply multiply by 2 to find the diameter. So let's go over our key points from today. As usual, make sure you get them in your notes so you can refer to them later. The area of an object is the amount of space enclosed in a two dimensional shape. We also saw that area is measured in square units, such as centimeters squared or inches squared. And we saw that we can use formulas for area to calculate either the area of a shape or the dimensions of that shape given the appropriate information.

So I hope that these key points and examples helped you understand a little bit more about area. Keep using your notes and keep on practicing, and soon you'll be a pro. Thanks for watching.

Terms to Know

The ratio of a circle's circumference to its diameter; approximately 3.14.

Formulas to Know
Area of Circle

A subscript c i r c l e end subscript equals pi r squared

Area of Rectangle

A subscript r e c tan g l e end subscript equals b h

Area of Triangle

A subscript t r i a n g l e end subscript equals 1 half b h