Difference between revisions of "AoPS Wiki:Sandbox"
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We want to find the area of this figure: | We want to find the area of this figure: |
Revision as of 20:30, 2 April 2014
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.
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
.
Hence, the area of the whole circle is , and the area of the 3/4 circle is
.
Adding it all up, we find the answer to be .
Just plug it into your calculator. And please understand where all the numbers came from before writing the answer down.