Answer
a) $A=56.9~ft^{2}$
b) $c=4.16ft$ or $49.9~in$
Work Step by Step
(a)
The area of the workstation is the area of the square minus the area of the circle formed by the 4 corner segments.
We use the formula $A=a^{2}-\pi r^{2}$
Where
$a=8ft$
$r=18in=1.5ft$ ($1~foot=12~inches$)
So,
$A=(8ft)^{2}-\pi (1.5ft)^{2}=56.93ft^{2}\approx56.9~ft^2$
(b)
The distance from the corner to the center of the workstation ($c$) is half the hypotenuse of the triangle formed by the sides of the table minus the radius of the corner.
Using the Pythagorean Theorem, we get:
$c=\frac{1}{2}\sqrt {(8ft)^{2}+(8ft)^{2}}-1.5ft=4.16ft$
We can convert this to inches as well ($12~inches=1~ft)$:
$4.16*12~inches=49.9~inches$
