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Math Help - Creating an Expression from an Object

  1. #1
    Newbie LaMandie's Avatar
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    Creating an Expression from an Object

    The question:
    "Write an expression for the surface area of this tent. Do not include the floor."

    Diagram of the tent:
    Creating an Expression from an Object-tent.jpg (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)
    = (x^2/8)

    put together: 4x^2 + (10x^2/8) + (x^2/8)
    = (32x ^2/8) + (11x^2/8)
    = 43x^2/8

    According to the book though, the correct answer is 45x^2/8.

    Where did I go wrong?
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  2. #2
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    front and back of the roof: x * [(5x/8)^2 - (x/2)^2]^(1/2)
    = x * [ (x^2/8) ]^(1/2)
    = (x^2/8)
    Both equalities are wrong here. (5/8)^2 - (1/2)^2 = 9/64, the square root of which is 3/8.
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  3. #3
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    Hello, LaMandie!

    Write an expression for the surface area of this tent. Do not include the floor.

    Diagram of the tent:
    Click image for larger version. 

Name:	tent.jpg 
Views:	19 
Size:	12.7 KB 
ID:	19936 (basically, a triangular prism on top of a cube.)


    My work so far:

    Sides of the tent (cube): . 4x^2 .Yes!

    Sides of the roof: . (\frac{5}{8}x)(2x) = \frac{5}{4}x^2 .Yes!
    Front and back of the roof: . x\bigg[ (\frac{5}{8}x)^2 - (\frac{x}{2})^2\bigg]^{\frac{1}{2}} \;=\: x \left(\frac{x^2}{8}\right)^{\frac{1}{2}} . no

    I think you forgot to square . . .

    . . x\bigg[\frac{25}{64}x^2 - \frac{1}{4}x^2\bigg]^{\frac{1}{2}} \;=\;x\bigg[\frac{9}{64}x^2\bigg]^{\frac{1}{2}} \;=\;x\cdot \frac{3}{8}x \;=\;\frac{3}{8}x^2

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