yego.me
💡 Stop wasting time. Read Youtube instead of watch. Download Chrome Extension

Scaling perimeter and area example 2 | Transformational geometry | Grade 8 (TX) | Khan Academy


2m read
·Nov 10, 2024

We're told quadrilateral A was dilated by a scale factor of 2/3 to create quadrilateral B. Complete the missing measurements in the table below. So like always, pause this video and then we will do this together. Try to do it yourself, and then we'll do it together.

All right, so in previous videos, we talked about if you have a scale factor, perimeter is going to be scaled by the same amount, while area is going to be scaled by the square of that. So perimeter is also going to be scaled by 2/3. So 30 * 2/3… let me write that a little bit neater. So times 2/3 is going to be 20.

Then the 54 is going to be scaled by (2/3) squared. One way to think about it is, you're scaling in each dimension by 2/3, and so when you multiply the two dimensions to get area, you're going to be multiplying by 2/3 twice to get the new scaled area. So what is (2/3) squared? Well, that is the same thing as 4/9. So what is 54 * (4/9)?

That is equal to 54 * (4 over 9). Both 54 and 9 are divisible by 9, so let's divide them both by 9. This becomes 6, and this becomes 1. So we end up with 6 * 4, which is equal to 24, and we're done.

Now to make this very tangible in your head, let's give an example of where this could actually happen. Let's imagine that quadrilateral A, let's say it looked like this, and I think I can eyeball it. Let's say that that dimension is 6, and that dimension is 9. I think that adds up: 6 plus 6 is 12, and 9 plus 9 is 18. So yes, this perimeter is 30, and the area here is actually 54.

So this is actually the example of quadrilateral A over here. And now quadrilateral B, if we're scaling it by 2/3, then all of these dimensions are going to be scaled by 2/3. So quadrilateral B will, instead of having a length of—or height of—6 over here, it's going to have a height of 4, and instead of having a length or width of 9 here, it's going to be 2/3 of that. It's going to be 6.

So the quadrilateral will look like this, and we can verify that the perimeter now is going to be 4 plus 4, which is 8, plus 6, plus 6, which is 12. So it's 8 plus 12, which is 20, and the new area is 6 * 4, which is 24. Now, you didn't have to do this, but I just wanted to make sure you understood why this was happening.

More Articles

View All
The Immune System Explained I – Bacteria Infection
Every second of your life, you are under attack. Billions of bacteria, viruses, and fungi are trying to make you their home, so our bodies have developed a super complex little army with guards, soldiers, intelligence, weapons factories, and communicators…
"EMPATHY" - другой взгляд на теннис
Hello, dear friends! Today I would like to make a video illustration of the word “empathy.” This word has a literal translation as compassion, sympathy. But in fact, the most important translation of this word is to understand the situation from the other…
15 Dumb Ways to Spend Your Money
Alex, do you ever find yourself, like halfway through the month, and wonder where your paycheck went? Well, you’re not alone. Okay, we all have those moments where we splurge a little bit too freely, sometimes in ways that might make us cringe later on. L…
Vlog: I counted almost $30,000,000 worth of cars in this parking lot!
What’s up you guys? It’s Graham here. So it seems like every 10,000 subscribers, I end up doing another vlog, and since I just hit 30,000 subscribers, here’s another vlog! I actually think it’s more like 34,000 by the time I’m actually doing this. I’m pro…
Warren Buffett:The upcoming stock market collapse?
Warren Buffett’s favorite stock market indicator is flashing warning signs. Warren Buffett’s called The Oracle of Omaha for good reason, and it is not just pure intuition. He coined a certain metric called the Buffett indicator, and he has even gone as fa…
LearnStorm Growth Mindset Livestream
Ask your kid, “What’d you do today?” or “What’d you do today at school?” “Nothing.” “How was it?” “Fine.” You know you always hear that, but if parents can be intentional about how they talk to their kids after school. I always ask my kids, and we hav…