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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.
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.