A set of seven built-in bookshelves is to be constructed in a room. The floor-to-ceiling clearance is 7ft 11 in. Each shelf is 1 in. thick. An equal space is to be left between the shelves, the top shelf and the ceiling, and the bottom shelf and the floor. How many inches should there be between each shelf and the next? (There is no shelf against the ceiling and no shelf on the
floor.)

  c.  9 units²

Step-by-step explanation:

The formula for the area of a trapezoid is ...

  A = (1/2)(b1 +b2)h

where b1 and b2 are the lengths of the parallel bases, and h is the height between them. From calculations using the coordinates, or from a figure, you can see that the base lengths area 3 units and 6 units, and the distance between them is 2 units.

Putting these numbers into the formula gives the area:

  A = (1/2)(3 units + 6 units)(2 units) = 9 units²