# Creating an Expression from an Object

• Dec 2nd 2010, 08:33 PM
LaMandie
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:
Attachment 19936 (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?
• Dec 3rd 2010, 03:39 AM
emakarov
Quote:

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.
• Dec 3rd 2010, 03:56 AM
Soroban
Hello, LaMandie!

Quote:

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

Diagram of the tent:
Attachment 19936 (basically, a triangular prism on top of a cube.)

My work so far:

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

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

I think you forgot to square . . .

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