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6th-8th Grade Math: Practice & Review55 chapters | 469 lessons

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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.

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.

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:

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.

*Find the area of this shape. The units are in feet.*

The nice thing about the counting method is that as long as the shapes are on grid paper or the coordinate plane, you can simply count the number of squares contained inside the shape. Counting the squares inside this shape, you get a total of 16 squares. So, the area of this shape is 16 square feet.

Let's try another one:

*Find the area of this shape. The units are in centimeters.*

You can see the shape does not have to be a rectangle or square. Here in this shape, you actually see a diagonal line. You see that this diagonal line is cutting your squares in half. So how do you count these? You count a half square for each square that is cut in half. You see four such squares cut in half, so your count will equal 2 whole squares for this part. You add this to the count of the other whole squares. The count of the other whole squares equal 18. So, your total count is 20 squares. The area of this shape, then, is 20 square centimeters.

What have you learned? **Area** is defined as the amount of space inside a two-dimensional object. The **counting method** of finding the area involves counting the number of squares inside the shape. It's actually a very simple process, which involves the counting of whole squares. These whole squares come from the units of the *x*- and *y*-axes on the coordinate plane or the squares on a grid paper. The units for area are always squared. Each square can represent any kind of measurement unit, either specified by the problem or by you.

Once you are finished, you should be able to:

- Define
*area* - Find the area of a shape using the counting method

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3 in chapter 33 of the course:

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6th-8th Grade Math: Practice & Review55 chapters | 469 lessons

- What is Perimeter? - Definition & Formula 8:31
- Perimeter of Triangles and Rectangles 8:54
- Area: Definition & Counting Method 4:06
- Measuring the Area of a Rhombus: Formula & Examples 6:30
- Measuring the Area of a Rectangle: Formula & Examples 4:40
- Measuring the Area of a Trapezoid 4:38
- Area of Triangles and Rectangles 5:43
- Go to 6th-8th Grade Measurement: Perimeter & Area

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