About this video
The shaded region is a 10 by 10 square with a quarter circle of radius 3 cut from each corner. Since four quarter circles make one whole circle, the shaded area is the square's area minus one circle's area: 100 - 9 pi square units.
You'll be able to
- find the area of a shaded region by subtracting the cut-out parts from a whole shape.
- see that four quarter circles with the same radius make one whole circle.
- write an answer like 100 - 9 pi in terms of pi.
Key words
- shaded region
- The colored part of a figure whose area you are asked to find.
- quarter circle
- One fourth of a circle, like a corner slice.
- radius
- The distance from the center of a circle to its edge.
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.
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