Explanation:
just think calm and logically.
what are the parts of the surface area ?
rest assured, there is no such thing like a general equation for the surface area of a prism.
well sure, there could be, but there are so many different variations, to describe them would be more complicated than the formula. so, we only have a general approach for the volume of such regular prisms (ground area × height).
but for the surface area we just have to break this problem into smaller problems we can easily solve and then add the results together.
so,
we see, there are 5 sides of this special prism.
top, bottom, left, right and front.
so, we need to calculate these 5 areas and simply add them up.
left and right are rectangles. one is
11×18 = 198 in²,
the other is
12×18 = 216 in², together they are 414 in².
the front is a rectangle
8×18 = 144 in²
top and bottom are equal triangles. each is
8 × height / 2
or per Heron's formula
A = sqrt(s(s -a)(s - b)(s -c)) where s = (a + b + c)/2
our s here is
s = (8 + 11 + 12)/2 = 15.5
A = sqrt(15.5×7.5×4.5×3.5) = sqrt(1830.9375) =
= 42.78945548... in²
both together are 85.57891095... in²
so, the total surface area is
414 + 144 + 85.57891095... = 643.578911... in²
if we need to round to e.g. whole square inches, this would be
644 in²