A double check of my answer. Involves geometry and algebra 
The $2$ slices cut into by Lee combine to make one big triangle. I used the Pythagorean theorem to find the length of the missing side (hypotenuse) to be $\sqrt{128}$, and I used the Pythagorean theorem again to find the length of the side John's slice borders with the other slice that Lee has cut into, the length is $\sqrt{32}$. Using this information, I just plug in the correct variables to the correct formulas to the answer to the question.
Apparently the area of a right triangle is $\frac{ab}{2}$$ so:
$$\frac{1}{2} \left(\frac{\sqrt{128}}{2} \cdot \sqrt{32} \right) = 16$$
So that's John's slice, now for Lee's:
Apparently, the area for an ellipse is: (half major axis * half minor axis * π) / 2 so...
$\frac{1}{2}\frac{\sqrt128}{2} (8 - \sqrt32)  π = 20.82$
That means
John's slice =  16
Lee's slice = 20.82
And the difference is 4.82, according to my math. But when I look at the answer key it agrees that Lee's pie is bigger but differs by how much, stating Lee's pie is only bigger by  2.265
Now funny enough, I can achieve the same decimal value of the prescribed answer by using the formula to find the area of a circle instead of an ellipsis. But clearly what I'm looking at is an ellipse, not a circle. So I'm thinking it's possible they used the wrong formula.
 A: The whole pizza is $64\pi$. As per your calculations the square formed by $8$ pieces as John's is $128$. The difference is $4$ times the size of Lee's slice. So, John's is $16$ and Lee's $16\pi-32\approx18.265.$ The difference is $2.265$
A: It's easier to recognize John's slice is a right triangle with two $45^\circ$ angles.  So it's sides are $s,s$ and $\sqrt 2 s$.  And the pizza has diameter $16$ the hypotenuse is $8 = \sqrt 2 s$ so $s =\frac 8{\sqrt 2}=4\sqrt 2$.  And the area is $\frac 12 s\cdot s = \frac 12 (4\sqrt 2)^2 = 16$ square inches.
Now the entire pie is $\pi r^2 = 64\pi$  there should be $8$ normal slices each $\frac {64\pi}8 = 8\pi$ square inches in area.  So one of those two parts of Lee's piece is a whole slice minus John's slice.  That's $8\pi - 16 = 8(\pi-2)$ square inches.  Lee has $2$ of those pieces so his part is $16(\pi-2)$ square inches.
As $\pi-2 > 1$ Lee's pieces are $(\pi - 2)$ times bigger.
The difference is $16(\pi - 2) - 16 = 16(\pi - 3)$.
I see utterly no reason to try to convert or estimate that as a decimal number but it is apparently what the book wants.  so $16(\pi-3) \approx 16(3.14-3)=16\cdot 0.14 = 1.6\cdot 1.4 = (1.5 + 0.1)(1.5-0.1)= 2.25 - 0.01= 2.24$ square inches roughly.
If we use a calculator I get Lee's slice is is $16(\pi -2)\approx  18.265482457436691815402294132472...$  (If I calculate by hand with $\pi \approx 3.14$ I get $18.24$ so that accounts for a difference of $0.025482457436691815402294132472...$ which is the aproximate value of $16 \times 0.0015926535897932384626433832795....$)  But such accuracy is ludicrously unimportant.
