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Course: Geometry (OPS pilot) > Unit 1
Lesson 7: Perimeter, circumference, and area- Find a missing side length when given perimeter
- Find perimeter when a side length is missing
- Perimeter word problem: tables
- Perimeter word problem: skating rink
- Perimeter word problems
- Area & perimeter word problem: dog pen
- Area & perimeter word problem: table
- Comparing areas word problem
- Area and perimeter situations
- Represent rectangle measurements
- Area & perimeter of rectangles word problems
- Decomposing shapes to find area: grids
- Understand decomposing figures to find area
- Decomposing shapes to find area: add
- Decomposing shapes to find area: subtract
- Decompose figures to find area
- Drawing a quadrilateral on the coordinate plane example
- Drawing polygons with coordinates
- Area of a parallelogram on the coordinate plane
- Area and perimeter on the coordinate plane
- Coordinates of a missing vertex
- Example of shapes on a coordinate plane
- Dimensions of a rectangle from coordinates
- Coordinates of rectangle example
- Quadrilateral problems on the coordinate plane
- Quadrilateral problems on the coordinate plane
- Parallelogram on the coordinate plane
- Radius, diameter, circumference & π
- Labeling parts of a circle
- Radius, diameter, & circumference
- Radius and diameter
- Radius & diameter from circumference
- Relating circumference and area
- Circumference of a circle
- Area of a circle
- Area of a circle
- Partial circle area and arc length
- Circumference of parts of circles
- Area of parts of circles
- Circumference review
- Area of circles review
- Finding circumference of a circle when given the area
- Area of a shaded region
- Impact of increasing the radius
- Circumference and rotations
- Area and circumference of circles challenge
- Shaded areas
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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 .(16 votes)
- i love the comments on this app 💀💀(8 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)
- 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) - Can you please explain me the formula because I don't understand?(3 votes)
- nobody does mate.(3 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)
- 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)
- 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)
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.