Problem of the Day

Chapter 11, Lesson 6

A designer is making cardboard props to be used as holiday decorations in a shopping mall. For each prop, the designer first makes a template on graph paper to show the construction of the faces of the finished prop. One of the props is in the shape of a rectangular prism.

The template for the top and bottom faces of the prism has its vertices at (0, 0), (0, 15), (30, 15), and (30, 0). The template for the front and back faces has its vertices at (0, 0), (0, 60), (30, 0), and (30, 60). The template for the side faces has its vertices at (0, 0), (15, 0), (0, 60), and (15, 60).

Write and evaluate an expression to find the surface area of this prop.