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Big Ideas Math Geometry: Online Textbook Help12 chapters | 142 lessons

Instructor:
*Yuanxin (Amy) Yang Alcocer*

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

After reading this lesson, you'll know how you can use the coordinate plane to help you find the perimeter and area of various shapes. Learn how you can find your answers just by counting.

In this lesson, you'll learn how you can use the coordinate plane to help you find the perimeter and area of various shapes. Remember, the **coordinate plane** is the grid that has an x-axis and a y-axis with points that are labeled with both an x-value and a y-value (x, y).

Usually, you use the coordinate plane to graph lines and curves, but you can also use it to help you find the perimeter and area of various shapes.

Let's take a look at how.

Let's look at finding the perimeter of a shape first. Remember, the **perimeter** of a shape is the distance around the shape. For example, a triangle's perimeter is the distance along all three sides of the triangle; it's the distance it takes to walk all the way around, ending up where you began. Likewise, a square's perimeter is the distance along all four sides.

You could use formulas to help you find the perimeter of these shapes, but you could also draw these shapes on the coordinate plane and then you could use the units of the coordinate plane to help you find the perimeter.

Say you are given this shape on the coordinate plane. You are then asked to find the perimeter.

The coordinate plane actually makes your job of finding the perimeter a whole lot easier. All you have to do to find the perimeter once your shape is drawn on the coordinate plane is to count your way around the shape. You are looking for the number of squares the perimeter of your shape takes up.

Looking at your shape, it looks like a rectangle, and the bottom side is taking up 5 unit squares. The top of the rectangle then is also 5 unit squares. The left and right sides take up 4 unit squares. Adding up all four sides, you get a total of 5 + 4 + 5 + 4 = 18 unit squares. So, that is the perimeter of your shape.

The coordinate plane also makes finding the area of a shape a lot easier. The **area** of a shape is the space inside the shape. Think of it as the amount of space the shape covers. Just like with the perimeter, when you use the coordinate plane to help you find the area, all you have to do is to count the number of squares. In the case of the area, you are counting the number of squares that are covered up.

Working with the same rectangle as before, the area, in this case, is 20 unit squares. You see the shape covering 4 rows of 5 unit squares. Adding them up, you get 5 + 5 + 5 + 5 = 5 * 4 = 20.

Remember, it doesn't matter where your shape is located on the coordinate plane, all that matters is how many squares the edges pass through for perimeter and how many squares the shape covers for the area.

Now, let's look at how this can help you when you are given a word problem.

Paul wants to paint a sign that looks like a house, so he needs to find the area of his house sign. He wants his sign to be 8 units wide and 12 units tall. He wants the roof part to be 4 units tall, so the bottom of the house should be a square that is 8 units tall. What is the area of this shape?

To use the coordinate plane to help you solve this problem, you first draw your shape on this coordinate plane. From the problem, you gather that you are drawing a square that is 8 units wide by 8 units tall and then a triangle on top of it to make the shape look like a house. The triangle is 8 units wide by 4 units tall.

To find the area of this shape, all you need to do now is to count the number of boxes that are covered by the shape.

The square, you can see, covers 8 rows of 8 units each for a total of 64 units for the square. For the triangle, you can see that the shape covers only half of some of the unit squares. When you see this, you'll want to add up your half squares; 2 half squares make up a whole square. If you are left with half a square, then your answer will have a 1 / 2 in it. Looking at your triangle, and counting, you count the number of unit squares that it covers as 7 units squares for the bottom row, then 5 unit squares for the row on top of that, then 3 unit squares, and then 1 unit square for the tip of the triangle. Adding these up you get 7 + 5 + 3 + 1 = 16 unit squares for the triangle. Now, adding the square and the triangle together, you get a total area for the shape of 16 + 64 = 80.

Let's review. The **coordinate plane** is the grid that has an x-axis and a y-axis with points that are labeled with both an x-value and a y-value (x, y). The **perimeter** of a shape is the distance around the shape. The **area** of a shape is the space inside the shape.

To use the coordinate plane to help you find the perimeter and area of various shapes, you first draw the shape on the coordinate plane and then you count the number of unit squares the shape takes up. For the perimeter, it's the number of unit squares that go around the shape. For the area, it's the number of unit squares that the shape covers up.

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Big Ideas Math Geometry: Online Textbook Help12 chapters | 142 lessons

- Undefined Terms of Geometry: Concepts & Significance 5:23
- Line Segments & Rays: Definition & Measurement 3:59
- Ruler Postulate: Definition & Examples 5:19
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- Line Segment Bisection & Midpoint Theorem: Geometric Construction 4:39
- How to Use The Midpoint Formula 3:33
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- Concave & Convex Polygons: Definition & Examples 3:43
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