Finding the Area of a Rectangle Using the Formula | Math with Mr. J

Welcome to Math with Mr. J. In this video I'm going to cover how to find the area of a rectangle using the formula for the area of a rectangle. Now in other area videos we talked about counting unit squares, adding up rows or columns, and multiplying side lengths to find area. So to add to this and take this a step further we're going to look at the formula for finding the area of a rectangle. So basically we're going to make this a little more official, a little more mathematical. Now we can think of a formula as a special rule we can use for a certain situation. For example our formula for the area of a rectangle is area equals length times width. We can use this formula, this special rule, to find the area of any rectangle. Let's jump into number one and see what this looks like. For number one we have a rectangle with side lengths of seven inches and five inches. Let's start by writing out our formula. So area equals length times width. I used a capital A for area and then a cursive L for length so it doesn't get confused with a one. Use what works best for you though as long as you know that that is an L. And then times W for width. Now we plug in our length and width. Well which side is the length and which is the width? The way I look at it length and width are used here to make it clear that we want to multiply the different side lengths. One of the side lengths times one of the other side lengths. For example for number one we need to use seven inches and five inches, those different side lengths. We can't use seven inches and then the other side that is seven inches and multiply those side lengths. That will not work. So we have two different names so to speak for those different sides length and width. Now keep in mind as long as we use one of the side lengths for the length and the other side length for the width we will get the correct area. Now one common way to go about this though is to use the longer side for length and the shorter side for the width. And that's what we're going to do for this video. So let's plug in seven inches for the length the longer side. So area equals seven inches times the width the shorter side length five inches. And now we multiply so we have seven inches times five inches. Seven times five gives us 35 and this is area so this is going to be square inches. And I'm going to use the abbreviation here so sq inches. This is the area of that rectangle. Now what happens if we do five inches times seven inches? Will that be incorrect? Well five inches times seven inches still gives us 35 square inches so we get the correct area that way as well. So you'll notice this is the same thing we've been doing to find the area of rectangles multiplying side lengths. But the formula makes this a little more official and organized. It gives us a special rule to go off of for all rectangles. Let's move on to number two where we have a rectangle with side lengths of 25 centimeters and four centimeters. So let's set this up area equals length times width. Now we plug in let's use 25 centimeters for the length so 25 centimeters times four centimeters for the width. Now we multiply 25 times four gives us 100. And we are working with centimeters here so this is square centimeters. The area of that rectangle is 100 square centimeters. Now keep in mind four centimeters times 25 centimeters will give us an area of 100 square centimeters as well. Let's try two more examples and move on to numbers three and four. Taking a look at number three we have a rectangle with side lengths of six yards and eight yards. So let's find the area here. We will start with our formula area equals length times width. We will use the longer side for the length so eight yards times the width six yards. Now we multiply eight times six gives us 48. And we are working with yards here so this is an area of 48 square yards. Lastly for number four we have a rectangle with side lengths of 11 meters and one meter. Let's start by writing out our formula so area equals length times width. Now one thing we do not want to do here is multiply all four side lengths. We do not want to do 11 meters times 11 meters times one meter times one meter. Even though we have all four side lengths labeled here we use one of the 11 meter side lengths and multiply it by one of the one meter side lengths. So we need to do 11 meters we will use that for our length times one meter for our width. 11 times one gives us an area of 11 and this is square meters. And that's the area of that rectangle. So there you have it there's how to find the area of a rectangle using the formula. Now is this the formula for finding the area of every shape? No there are different formulas for different shapes. For example we have a different formula to find the area of a triangle and a different formula to find the area of a circle. This video focused on rectangles. I hope that helped. Thanks so much for watching. Until next time, peace.