The given solid is a prism. To calculate the surface area of a prism, we can use the known formula where P is the perimeter of the base, h is the height, and B is the area of the base.
S=Ph+2B
The base of a cube is a square, this means that the base has four equal side lengths. Let's add them to find the perimeter of the base.
P&=s+s+s+s
P&= 4 s
Now, we can calculate its area using the formula for area of a square.
B&= s * s
B&= s^2
Finally, we have enough information to find the length of a lateral edge of the cube. Let's substitute S with 294 square inches, P with 4s, h with s, and B with s^2 into the formula.
