Tough question both per se both to figure out a simpler way to deal with



we know that the radius is 7 and therefore the diameter is 14. At the same time the diameter is also the diagonal of the rectangle.

S the chord is 6. Also the base of the triangle is the radius of the circle and it is 7

Now we can use the Heron's formula to calculate the height

$Area=\frac{7+7+6}{2}=\frac{20}{2}=10$

$Area=\sqrt{10(10-7)(10-7)(10-6)}=\sqrt{10*3*3*4}=18.9$

$18.9=\frac{1}{2}*7*h$

$h=5.4$

Double the height of the triangle and you have the length of the rectangle $5.4*2=10.8$ (this is a huge estimation by myself)

Now we have the diagonal 14 and the length 10.8 and we can calculate the width

$w=\sqrt{14^2-10.8^2}=\sqrt{196-116.64}=\sqrt{79.36}=8.9$

Now the area of rectangle is $8.9*10.8=96$

However, I worked by estimation. So clearly the numbers are inferior than that and because the last two answer are pretty close (95,96) I personally during exam I would be pretty sure the answer is C

sorry it is the only way to make it more simple to reach the solution

Thanks for the explanation Carcass, but does such lengthy questions generally show up in GRE?

That's a good question.

I think no because too many steps are involved.

However, it is still good for practice to reinforce your mental muscles.

Regards