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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
• 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 .
• i love the comments on this app 💀💀
• at what was that green thing
• 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:)
• How do you find the area of a circle?
• A=π r^2 (pi times radius squared).
• 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
• Can you please explain me the formula because I don't understand?
• nobody does mate.
• How do you find the area of a shaded area if the shaded area is part of a circle?
• 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?