Computing Volume from Cross-Sectional Area

[pilotsjs89]

Homework Statement

A house attic has rectangular cross sections parallel to the ground and triangular cross sections perpendicular to the ground. The rectangle is 30 feet by 60 feet at the bottom of the attic and the triangles have base 30 feet and height 10 feet. Compute the volume of the attic.

Homework Equations

The Attempt at a Solution

I know how to solve this once it is set up as an integral, but I am having trouble setting up the integral itself.

 

[Avodyne]

An integral is overkill. Think of slicing the attic into triangular slabs, each one foot thick. What is the volume of each slab? How many slabs are there?