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## 7th grade

### Course: 7th grade>Unit 9

Lesson 2: Area and circumference challenge problems

# Area of a shaded region

Here's a fun one: find the area of a shaded region where you first determine the area of a square and then the area of a circle. Created by Sal Khan.

## Want to join the conversation?

• This may not sound very smart but why did you multiple 3*3
(14 votes)
• Sal multiplied 3 and 3 because the formula for getting area is A = r^2 pi. If our radius is 3, and if part of the formula is r^2, to get the radius to the second power you multiply 3 and 3 .
(13 votes)
• i love the comments on this app 💀💀
(6 votes)
• Same So entertaining to read peoples comments 😂
(2 votes)
• at what was that green thing
(5 votes)
• It is due to an incomplete answer. Once you finish typing your answer, assuming it is an acceptable form for the particular question, the green guy goes away:)
(3 votes)
• Why he didn't multiply it by 4 like:
100 - 4(3^2)pi? isn't this going to give us all four sides? o.O #confused

PS: Oh I get it, I get it now :D. (3^2)pi will give us the entire area of full circle :D
(4 votes)
• How do you find the area of a circle?
(2 votes)
• A=π r^2 (pi times radius squared).
(4 votes)
• Can you please explain me the formula because I don't understand?
(2 votes)
• nobody does mate.
(3 votes)
• Why don't you multiply by four at the end instead of just 9π? Aren't you solving for four sides then subtracting?
(3 votes)
• find the area of shaded region of square 6cm
(3 votes)
• how am i supposed to do this? i cant do 40pi and i cant use a calculator?
(2 votes)
• What if your book doesn't give the area of the shape?
(2 votes)

## Video transcript

We're asked to find the area of the shaded region, so the area of this red-shaded region. So this is interesting. This is almost a 10 by 10 square, except we have these quarter circles that are cut out. So the area of this would be the area of what a 10 by 10 square would be minus the area of these quarter circles. And each of these quarter circles is a quarter of a circle with a radius 3. I think we can assume that all of these, if you took the distance from here to the outside of this quarter circle, have radius 3. So if you put four quarter circles together, you're going to have a complete white circle. So one way to think about this is that the area of this whole red region is going to be the area of the entire square, which is 10 by 10. So it's going to be 10 times 10, which is 100 whatever square units we have. And then we're going to subtract out the area of the four quarter circles. And that area is going to be equivalent to the area of one circle with a radius of 3. So what's the area of a circle with radius 3? Well, the formula for area of a circle is pi r squared, or r squared pi. So the radius is 3. So it's going to be 3 times 3, which is 9, times pi-- 9 pi. So we have 100 minus 9 pi is the area of the shaded region. And we got it right.