help surface area of 3d rectangle

[jzw]

Seems pretty straightforward - but what am I doing wrong? Step by step in figuring this out?

What is the surface area of a rectangle that is 12 ft long, 4 ft wide and for which the greatest possible (straight line) distance between any two points is 13 ft?

A. 96
B. 144
C. 169
D. 192
E. 624

[pemdas]

A polygon is not a rectangle, but a rectangle is a polygon. We are given width, length and need to find height, which is according to deluxe formula d^2=a^2+b^2+c^2. Here d is assumed the straight line=13 and a=12,b=4,c=? The required will be 2(12*4)+2(4*c)+2(12*c)

Solution: 13^2=12^2+4^2+c^2 and c^2=169-160=9 where c=3
The required is found as 2(12*4)+2(4*3)+2(12*3)=192

d

Seems pretty straightforward - but what am I doing wrong? Step by step in figuring this out?

What is the surface area of a rectangle that is 12 ft long, 4 ft wide and for which the greatest possible (straight line) distance between any two points is 13 ft?

A. 96
B. 144
C. 169
D. 192
E. 624