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- anonymous

Which formula represents the subtracted portion of the surface area formula for the shape below? Assume that all rectangular faces are squares.
Three figures join to make a composite solid. On the left, a square based pyramid is attached to the top of a cube. The right side of the cube is attached to the side of a triangular prism.
four s squared
one-third s squared h
one-third s squared h plus one-half s square h
s h
fan
i wil try to draw

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- anonymous

- katieb

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- anonymous

|dw:1438540221597:dw|
sorry this is not very good

- phi

I'm not sure what you (they) mean by
" the subtracted portion of the surface area formula "
I would *guess* it means the "hidden" sides of the square covered by the pyramid and prism"
but that would be \( 2s^2\). But that does not match any of the choices.

- mathstudent55

|dw:1438546775095:dw|

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- mathstudent55

|dw:1438546923233:dw|

- mathstudent55

|dw:1438547009110:dw|

- mathstudent55

@phi
If you were to find the total surface area of the composite solid, you could find the total surface area of each component, the cube, the pyramid, and the prism.
Then you'd have to subtract the area of 4 square faces.
It is \(4s^2\) because there are two faces of the cube hidden (top and right), one face of the pyramid hidden (bottom base), and one face of the prism hidden (left square).
Altogether there are 4 hidden square faces.

- phi

ok, that makes sense. we subtract double the "hidden faces"

- mathstudent55

Exactly.

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