Area #3

Calculus Level 5

Consider a square with vertices at ( 1 , 1 ) ; ( − 1 , 1 ) ; ( − 1 , − 1 ) ; ( 1 , − 1 ) (1,1);(-1,1);(-1,-1);(1,-1) . Let S S be the region consisting of all points inside the square which are nearer to the origin than to any edge. The area of S S is A B ( C D − E ) {\frac{A}{B}(C\sqrt{D}-E)}

where A , B , C , D , E A,B,C,D,E are integers,_need not be distinct and D D is square free and A , B A,B are co prime.

Find A + B + C + D + E A+B+C+D+E


The answer is 18.

Tanishq Varshney by Tanishq Varshney , 23, India

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1 solution

Bob Kadylo
May 3, 2018

This general result is worth sharing: see here

In our specific problem, use L=2 and then A=4, B=3, C=4, D=2 and E=5. The sum is 18 \boxed {18}

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