



 
Hi Paul, I see you attic as composed of two pieces, a rectangular pyramid where the apex of the pyramid is not above the center of the rectangle and a dormer $PQRS.$ The volume of the attic is the sum of the volumes of the two pieces.The volume of each of these pieces can be calculated from a theorem I have always found surprising.
The rectangular pyramid part of your attic is such three dimensional region. The region $A$ in the plane is a 29 feet by 37 feet rectangle and $h$ is 3.5 feet. Hence the volume of this part of your attic is \[\frac13 \times (29 \times 27) \times 3.5 \mbox{ cubic feet.}\] The dormer is also a region whose volume can be calculated in a similar fashion. Think of the triangle $SQR$ as the base and $S$ as the point not in the plane of the base. The height of $S$ above the base plane is the length of $PS.$ The base of the triangle is $QR$ which has length 29 feet and its height, the perpendicular distance from $QR$ to $S$ is 3.5 feet. Hence the area of the triangle $SQR$ is $\large \frac12 \normalsize \times 27 \times 3.5$ square feet. Finally the volume of the dormer is \[\frac13 \times \left(\frac12 \times 27 \times 3.5 \right) \times 7 \mbox{ cubic feet.}\] I hope this helps,  


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