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Area: Definition & Counting Method

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  • 0:01 The Area
  • 0:40 Counting Method
  • 2:25 Example 1
  • 2:45 Example 2
  • 3:25 Lesson Summary
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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Watch this video lesson to learn what area is and how you can count to find the area of certain shapes. You will see how you can use blocks to help you visualize the problem and find your answer.

The Area

In this lesson, you will learn how to find the area of various shapes. What is area? Area is defined as the amount of space inside a two-dimensional object. Usually, these objects are your shapes, such as rectangles, triangles, squares, and circles. So, if you drew one of these shapes on a piece of paper, the amount of space contained in one of these shapes is the area of that shape. This amount of space could be bigger than the actual amount of paper space contained inside the shape if the shape drawn represents something larger. There are various ways of finding the area. The method that you will learn in this lesson is called the counting method.

Counting Method

The counting method of finding the area involves counting the number of squares inside the shape. Where do these squares come from? If you draw your shapes on grid paper or on a coordinate plane, then these squares come from the units on the x- and y-axes. Each square represents one square unit of the grid. Each unit can represent centimeters or inches or any other measurement unit. Which measurement unit each square represents depends on the problem or what you have specified each square to be. For example, this rectangle drawn on the coordinate plane has an area of 8 square inches because it contains 8 squares and each square is specified to be 1 square inch:

counting method

You can count the squares one by one and you will find 8 squares. Hence, the name of this method: counting method. There is one thing that you have to be super careful about and that is the units. Notice how I put that the area inside this rectangle is 8 square inches. Notice the word square. Whenever you are working with area, you have to use this word for all your units. So, if your units are feet, you have to say square feet. If your units are centimeters, then you have to say square centimeters.

The counting method is not suitable for calculating all areas. Specifically, the counting area is useful for calculating the area of those shapes that can be drawn nicely on the coordinate plane. It is possible to draw things to scale on the coordinate plane. In this case, you can set each square to be equal to your scale. For example, if 1 inch is equal to 12 inches in your scale, you can set each square to be equal to its scaled area of 12 * 12 = 144 square inches. Let's look at a couple more examples now.

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