A. He used 26 instead of 24 as the slant height of one set of lateral faces. B. He omitted the rectangle where the upper and lower solids join together. C. He included the 34 by 20 base of the figure.
Sure, let's analyze the given expression step by step to identify the errors Devon made.
The expression Devon used to find the surface area is: [tex]\[
2\left[(9 \times 20) + (9 \times 34)\right] + (34 \times 20) + 2 \left[\frac{1}{2} (20 \times 24)\right] + 2 \left[\frac{1}{2} (34 \times 26)\right]
\][/tex]
### Step-by-Step Analysis:
1. First Term: [tex]\(2(9 \times 20)\)[/tex] - This term calculates the area of two rectangles with dimensions [tex]\(9 \times 20\)[/tex].
2. Second Term: [tex]\(2(9 \times 34)\)[/tex] - This term calculates the area of two rectangles with dimensions [tex]\(9 \times 34\)[/tex].
3. Third Term: [tex]\(34 \times 20\)[/tex] - This term represents the area of a base with dimensions [tex]\(34 \times 20\)[/tex].
4. Fourth Term: [tex]\(2 \left[\frac{1}{2} (20 \times 24)\right] \)[/tex] - This calculates the area of two triangles with base [tex]\(20\)[/tex] and height (slant height) [tex]\(24\)[/tex].
5. Fifth Term: [tex]\(2 \left[\frac{1}{2} (34 \times 26)\right] \)[/tex] - This calculates the area of two triangles with base [tex]\(34\)[/tex] and height (slant height) [tex]\(26\)[/tex].
### Errors Identified:
1. Incorrect Slant Height: - When calculating the area of the triangles in the fifth term [tex]\(2 \left[\frac{1}{2} (34 \times 26)\right] \)[/tex], Devon used 26 as the slant height instead of the correct slant height of 24. - This is an error because the slant height used in the two sets of triangles should be consistent.
2. Included the Base Rectangle: - The term [tex]\(34 \times 20\)[/tex] represents the area of a rectangle which is the base of the figure. - Devon included this base in his calculation, which should not be included when calculating the surface area of the lateral faces and the upper solid.
3. Omitted the Joining Rectangle: - There is a rectangle where the upper and lower solids join together that Devon omitted in his expression. - This omission means that there was a missing component in the surface area calculation.
### Conclusion: Based on our detailed analysis above, Devon made the following errors:
1. He used 26 instead of 24 as the slant height of one set of lateral faces. 2. He included the [tex]\(34 \times 20\)[/tex] base of the figure. 3. He omitted the rectangle where the upper and lower solids join together.
Thus, the errors Devon made are accurately represented by the following statements:
- He used 26 instead of 24 as the slant height of one set of lateral faces. - He omitted the rectangle where the upper and lower solids join together. - He included the [tex]\(34 \times 20\)[/tex] base of the figure.
