The below Mathcounts mini presents two methods.
Circle and area revisited from Mathcounts mini
The first question is exactly the same as this one.
Besides the two methods on the videos, you can also use the following methods.
Solution III:
You can also look at this as a Venn Diagram question.
One quarter circle is A and the other is B, and both are congruent. (center at opposite corner vertexes)
The overlapping part is C.
A + B - C = 6^2 so C = A + B - 36 or 18pi - 36
Solution IV: which is 6 x 12 minus, the area of the half circle with a radius 6, you get the two white spots that are un-shaded.
Use the area of the square minus that will again give you the answer.
\(6^{2}-\left( 6*12-\dfrac {6^{2}\pi } {2}\right)\)
= 18pi - 36
Similar triangles and triangles that share the same vertexes/or/and trapezoid
Another link from my blog
Similar triangles, dimensional change questions are all over the place so make sure you really
understand them.
Take care and happy problem solving !!
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