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### Course: 7th grade (Illustrative Mathematics) > Unit 3

Lesson 6: Lesson 9: Applying area to circles# 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(15 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 .(17 votes)

- i love the comments on this app 💀💀(9 votes)
- Same So entertaining to read peoples comments 😂(0 votes)

- at1:05what was that green thing(6 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)

- Can you please explain me the formula because I don't understand?(4 votes)
- nobody does mate.(5 votes)

- How do you find the area of a circle?(3 votes)
- A=π r^2 (pi times radius squared).(5 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(5 votes) - How do you find the area of a shaded area if the shaded area is part of a circle?(3 votes)
- you figure out what the area of the circle is then subtract whatever percentage you need to(1 vote)

- I keep coming back to this video to understand how to use his methods in the area of shaded regions questions. And I keep getting stuck at the subtracting part. Let me explain with an exp of how the hint said to solve.

Let’s say we have A square and the length and with is 3cm so 3cm x 3cm, which equals 9cm^2

Boom. Done with that.

There is a circle on the inside that’s 1cm, for that we need to solve its area

The formula is A= pi*r^2

Plug in : A= pi x 1cm x 1cm (dunno why we are multiplying it 2x, again this is from the hint so I’m expressing my confusions as I go) so that equals to 1picm^2

And now we subtract the inner from the outer which is

9cm^2-1picm^2 which apparently equals to (it wasn’t an actual equal sign it was the about equal to sign) 5.86cm^2. The question also asked to round I believe but when solving by myself I didnt even get an answer similar, So How? the multiplying each regions part I understand but when it comes down to subtracting it doesn’t make sense. I even wrote it down separately and tried to figure out how it 5.86cm^2 and cannot figure it out. Please help what am I missing?(3 votes) - how do you find the area of a shaded region of a circle in a circle, the area being the larger circle subtracting the smaller cirlce(3 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.