SOLUTION: I have a word problem that I don't understand. It says what is the surface area in square feet? Rectangle 4 feet end of container is square, one side is 4 ft, other 3 sides is 4 ft

Question 890597: I have a word problem that I don't understand. It says what is the surface area in square feet? Rectangle 4 feet end of container is square, one side is 4 ft, other 3 sides is 4 ft. 9 ft long length....

I am not sure if the formula would be: L x W or 2LW + 2 LH + 2WH
Could you please get me on the correct path?
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
do you have a diagram? student answers no
Word for word what is the word problem? problem as stated by student
given this information that the geometric shape is a container
there are 4 sides and a top and bottom
let SA be surface area (we assume the top of the container is closed)
the top and bottom are trapezoids
we need to find the surface area of one of the trapezoids
trapezoid SA = ((b1 + b2) /2) * h where b1 and b2 is bases (parallel segments) and h is height
we know the length of b1 and b2, we need to find h
draw parallel lines from each end of the 4 foot side to the opposite 9 foot side
there are two right triangles, and the opposite 9 foot side = 4 + x + y
using Pythagorean theorem we have two formulas
x^2 + h^2 = 81
y^2 + h^2 = 81
then x^2 + h^2 = y^2 + h^2
x^2 = y^2
x = y
x = 5/2 = 2.5
y = 5/2 = 2.5
we can now solve for h
(2.5)^2 + h^2 = 81
h^2 = 81 - 6.25 = 74.75
h = 8.645808233
SA = 4*4 + 3*(4*9) + 2*( ( 9 + 4) /2) * 8.645808233)
SA = 16 + 108 + 112.395507029
SA = 236.395507029 square feet

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