Area of square inside circle

[woox]

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I was doing Topscore and came across this problem.

My question is the equation they used to find the area of square with the diameter value:

(d^2)/2

Is this equation good for all problems of this type?

 

[rockclock]

Yes.

if you're interested...

if you split the original square in half along the diagonal and then draw in the square that would be d^2, you can see that the smaller square consists of two of those triangles and the bigger one consists of four of them...hence, it's d^2/2 (or the algebra would give the same answer pretty quickly too)