How to Calculate Perimeter on a Coordinate Plan

In this video lesson, let us learn about real life applications of the coordinate plan. The problem given to us says that the vertices of a rectangle, that’s a rectangle, are located at the points (-3 and 2), (4 and 2), (4 and -3) and (-3 and 3). So we are given these four coordinates right? This four coordinates have been given to us. They describe a rectangle. We need to compute the perimeter of the rectangle and the area of the rectangle. So let’s do this. I drew a coordinate plan below and have already marked the four points. Let me show you how I did that. I took the first coordinate which is (-3, 2), so we started with zero we moved left three units because this first number is always the X-axis. So I go to (-3) on the X-axis and then (+2) on the Y-axis and that was my first point, okay? Similarly I marked (4, 2) which was here, (4) across the X-axis and (2) across the Y-axis, alright? (4, -3) which was (4+) and (-3) and then fourth point was (3, -3), okay? So I got these four points, these are the vertices of a rectangle. So let’s do this. Let’s join these and form the rectangle. I am just joining the four points that we marked —the coordinates that we marked. This is a rectangle right? What is the perimeter and what is the area of the rectangle? So we need to find the perimeter of the rectangle. What is the perimeter? Perimeter is the length of all sides, okay? So let us try and compute the length of the sides. What’s the length of the side? Well, let’s try and count it. It is 1 unit, 2, 3, 4, 5, 6, 7 units right? If I count the number of squares between the left and in the right end, there would 7 squares—one, two, three, four, five, six, seven—so the length of this rectangle is 7 units right? What’s the width of the rectangle? It is 1, 2, 3, 4, 5, —the width of the rectangle equals 5 units, right, we can see that. Starts at (+2) ends at (-3) so (2, -3), what’s the difference between them? It is 5 units right? If I add 5 to -3 I get +2. Anyway, so we found the length and the width. Now that we know the length and width, what’s the perimeter? All the perimeter is the length here which is 7 plus this which is 5 plus this which is 7 and this which is 5. So the perimeter (P=7+5+7+5) units, the length of each of the sides, right? Another way to do this is (2L+ 2W) it gives you the same thing right? What is it? (2xL) is (14+ 2W) is 10, it is 24 units okay? So the perimeter is 24 units.
Now let’s create a little bit of extra space and try and find the area of this rectangle. The area of a rectangle is (LxW), okay? (7x5) is 35 units squared because it is 7 units times 5 units, so the unit becomes units square. There is another way for us to do this. I can count the total number of squares that cover the inside of the rectangle— 1, 2, 3, 4, 5, 6, 7—similarly 7 here—7 here, so that is 7, 14, 21 + 7, 28 + 7, 35 that’s how I get to it. 7 units times 5 units which is 35 units².