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## 7th grade

### Course: 7th grade > Unit 6

Lesson 2: Area and circumference challenge problems# Area of a shaded region

CCSS.Math:

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 .(12 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:)(4 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) - What if your book doesn't give the area of the shape?(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)
- So wait, in this situation, how could u have found the area of the shaded region with the diametrr or is there no possible way?(2 votes)
- Find the shaded area of a triangle(1 vote)
- Area of a triangle is base times the height and then divide the base times the hight by 2. for example a triangle with a base of 3 and a height of 5 would have an area of 7.5.(3 votes)

- On1:23why did you put pi for the answer?(1 vote)
- When you are dealing with circles, there are two possible answers. If you use pi in the answer, it is an exact answer which mathematicians often use as correct. This is the answer that Sal ends on. There could also be an approximate answer by using some approximate value of pi. For example, we may want to know how much material you would need to build it.(2 votes)

- Also, what is the name of Sal's Khan Academy account?(1 vote)
- You can visit his profile at https://www.khanacademy.org/profile/sal/(1 vote)

## 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.