"Write an expression for the surface area of this tent. Do not include the floor."
Diagram of the tent:
(basically, a triangular prism on top of a cube.)
My work so far:
sides of the tent (cube): 4x^2
sides of the roof: (5x/8) * 2x = (10x^2/8)
front and back of the roof: x * [(5x/8)^2 - (x/2)^2]^(1/2)
= x * [ (x^2/8) ]^(1/2)
put together: 4x^2 + (10x^2/8) + (x^2/8)
= (32x ^2/8) + (11x^2/8)
According to the book though, the correct answer is 45x^2/8.
Where did I go wrong?