Scaling perimeter and area example 1

0:00- [Instructor] We're told, "Pentagon A was dilated by a scale factor of 3 to create Pentagon B. Complete the missing measurements in the table below." So pause this video, have a go at this before we do this together. All right, now let's work on this together.

0:14It's really just trying to ask us how does perimeter or area scale when you have a scaling factor? Because if we know that we can figure out what these squares are. And to help us with that, I will do a simpler figure first before we think about a pentagon. Although, the same principles will apply.

0:30Let's imagine we have a rectangle. So let's say this is our, actually, let me make it a little bit smaller. Let's say this is our original rectangle right over here. And let's say the long side, the length there is 2. And then the short side, the height there is 1.

0:51So the perimeter, I'll just write P for perimeter right over here, it's gonna be 2 plus 2, which is four, plus 1 plus 1, it is 6. And now what is its area? Its area is gonna be 2 times 1. It's going to be 2 square units. Now, let's imagine that we dilate it by a scale factor of 3.

1:11So then what are we going to be looking at? Well then we would be looking at something that looks like this. Let me do this in a different color, and I'm not obviously going to be able to do it exact, but it would look something like this. So that side was 1. Now that side is going to be 3.

1:28We've scaled it up by 3. This side was 2. Now this side is going to be 6. And similarly, that side was 1. Now that side's going to be 3. And let me just complete the rectangle there. So now when we scale it up, when we have a scale factor of 3, what is our new perimeter now?

1:49Our new perimeter is going to be 6 plus 6, which is 12, plus another 3, plus another 3, so plus another 6. So our new perimeter is going to be 18. And what's our new area? Our new area, or the area of the scaled rectangle is 6 times 3, which is 18. So what happened here?

2:12So our perimeter scaled up by the same as the scale factor. Our scale factor is 3 in this example, and our perimeter scaled up by 3. But here, the area did something different. Our area scaled up by 9. And actually, what it's scaling up by is 3 squared, which we know is 9.

2:33Because if you increase in the, let's call it one dimension by a scale factor, you're also doing it by the other dimension. And so if they're both scaled by 3 when you do the area, you're going to be scaling it times 3 twice, or 3 squared. So if we have a scale factor of 3, perimeter is going to be scaled by 3, by 3, so the new perimeter is going to be 33.

2:59Now, area, as we just said, that's going to be scaled by a factor of 9. So if our new area is 72, our old area was 72 divided by 9, which is going to be equal to... 8. And we are done.