AoPS Wiki:Sandbox
Welcome to the sandbox, a location to test your newfound wiki-editing abilities.
Please note that all contributions here may be deleted periodically and without warning.
In the computer world, a sandbox is a place to test and experiment -- essentially, it's a place to play.
This is the AoPSWiki Sandbox. Feel free to experiment here.
Warning: anything you place here is subject to deletion without notice.
[This was deleted due to its inappropriateness.]
test
---experimenthere-----
Please do not delete from this point on until 5:00 PST on 4/2!
We want to find the area of this figure:
We label the circle as circle C. We can break the figure into three parts, shown as the 3/4 circle, the triangle, and the rectangle.
Lets first take a look at the rectangle.
It has an area of .
Lets now take a look at the triangle, after drawing the height.
We see that both the radii are the two shorter sides of the triangle, making this a isosceles 45-45-90 triangle.
We also see that the height that we drew is half the hypotenuse(note the two smaller 45-45-90 isosceles triangles).
Hence, the area of the triangle is .
Now, let's take a look at the 3/4 circle. We know it is 3/4 because there is a 90 degree triangle cut out of it.
We find the radius using the 45-45-90 triangle. Since the ratios of the sides are 1:1:, we can find the radius to be .