Introduction to Area: Rectangles

[One speaker.]

[A slide is presented with the title “Introduction to Area”]

Female Speaker: Welcome to the introduction to area. [Turns to the next slide with a blue square in the top left corner.] Area is the amount of space on a flat surface. In order to define area, we first must define a unit square. A unit square is simply a square where each side is 1 unit length. [Writes “1 unit” on the right and bottom side of the square.]

If we’re talking about centimeters, this square is 1 centimeter by 1 centimeter. If we’re in feet, this square is 1 foot by 1 foot. If we're using inches, the unit square is 1 inch by 1 inch.

[Turns to the next slide with a blue square in the top left corner and an orange square on the right taking half of the slide with 12, 1 unit squares inside of it.]

Now let’s suppose we’re making a rug that is 4 feet long by 3 feet wide. [Writes “4 ft” on the bottom side of the orange square and “3 ft” on the left side.]  What is the area of this rug? Well in this case our unit square is 1 foot by 1 foot. [Writes “1 ft” on the right and bottom side of the blue square.]

Notice, we have already broken this space up into foot increments. This is 4 feet long and 3 feet wide. So the total number of unit squares that would fit on this rug is 12. [Numbers 1-12 start to appear on each square in the orange square.]  Notice that 3 x 4=12. [Writes “3x4=12” on the bottom left corner.]

So the length times the width equals the area, [Writes “LxW=Area” below “3x4=12”. The following information appears on the screen after the instructor is done writing : “Area=Length x Width.] or in other words, the area is equal to the length times the width. [“Area=Length x Width” fades out.]

And because we are using a square unit, the unit for area are units squared, [Writes “Units^2.] often written with two as the exponent. So the area of our rug is 3 feet times 4 feet, which equals 12 feet squared, [Writes out “3 ft x 4 ft = 12 ft^2.] or in other words 12 square feet.

[Next slide is presented with a blue square in the top left corner and an orange square on the right  with 6, 1 unit squares.]

Now, let’s suppose we are taking the measurement of a small little space that is 3 centimeters by 2 centimeters. [Writes “3cm” on the bottom side of the orange square and “2 cm” on the right side.]

In other words, between here and here [Draws a small line at the start of a 1 unit square and at the end and writes “1 cm” and repeats for the rest of the bottom side squares.] is one centimeter, and to here again is another centimeter, 1centimeter, and to here again is one more centimeter, so for a total of 3 centimeters. [Repeats the same thing as the bottom but on the right side of the square.] The same is true over on the side: 1 centimeter and another centimeter.

In this case, our unit square is 1 centimeter by 1 centimeter [writes “1cm” on the right side and bottom of the blue square.] because we’re using centimeters. So the area of this little space is the sum of all of the square centimeters that would fit in that space.

[Starts numbering the squares inside the orange square.] So 1, 2, 3, 4, 5, 6. 6 square centimeters. But again, 6 is the same as 2 times 3, [Writes “2x3”.]  or in other words 2 centimeters times 3 centimeters equals 6 centimeters squared [Writes “2 cm x 3 cm = 6 cm^2”.] because it’s not just a straight centimeter, it’s actually a square centimeter. And the total area contains 6 of those squares. So, 6 centimeters squared.

[End of Video.]