Question

devon studied the composite figure. he believed the surface area, in square units, could be found by simplifying the expression ( 2((9)(20)) + 2((9)(34)) + (34)(20) + 2(\frac{1}{2}(20)(24)) + 2(\frac{1}{2}(34)(26)) ). what error did devon make? he included the 34 by 20 base of the figure. he used 26 instead of 24 as the slant height of one set of lateral faces. he believed the upper part of the figure was a pyramid instead of a prism. he omitted the rectangle where the upper and lower solids join together.

Explanation:

Step1: Analyze the surface area formula

The formula for the surface area of a composite figure should account for all outer - facing surfaces. When two solids are joined, the area of the joining face is not part of the surface area.

Step2: Check the formula components

In Devon's formula \(2((9)(20))+2((9)(34))+(34)(20)+2(\frac{1}{2}(20)(24))+2(\frac{1}{2}(34)(26))\), he included the \(34\times20\) base. But this base is an internal face (where the two parts of the composite figure are joined), so it should not be part of the surface area calculation.

Answer:

He included the 34 by 20 base of the figure.