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Perimeter & Area in the Coordinate Plane

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.

The Coordinate Plane

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).


perimeter and area in coordinate plane


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.

Perimeter

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.


perimeter and area in coordinate plane


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.

Area

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.


perimeter and area in coordinate plane


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.

Word Problem

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.


perimeter and area in coordinate plane


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