Im doing so bad already i need a good grade. in the square below, the four quarter-circles are congruent. find the area of the shaded region. if necessary round your answer to two decimal places. wrong answers will be reported

I'm assuming a quarter-circle is exactly 1/4 of a circle.  Thus if you have 4 congruent quarter-circles, that should mean they make a complete circle.

If that is the case, then we can find the area of the full circle using pi*r^2.

So the area of the circle is 5^2*pi or 25pi.

To find the area of the shaded region, we subtract the area of the circle from the area of the square.

The area of the square is 10^2 or 100.

So the area of the shaded region is 100 - 25pi.

My calculator says that equals roughly 21.46

 C) 5

Work Shown:

s = square side length

A = area of square = 9x^2+12x+4

A = s^2

A = (ax+b)^2

A = a^2*x^2 + 2abx + b^2 apply the FOIL rule

A = 9x^2 + 12x + 4

Equating corresponding terms, we see that,

a^2*x^2 = 9x^2 which shows that a^2 = 9 and that solves to a = 3, assuming 'a' is positive.2abx = 12x leads to 2ab = 12 or ab = 6. Using a = 3 we can find that b = 2.b^2 = 4 solves to b = 2 which matches with the previous value of b found.

Using a = 3 and b = 2, the sum of the values is a+b = 3+2 = 5, so that's why the answer is choice C.

Side note: 9x^2 + 12x + 4 factors to (3x + 2)^2