The cross section of a trench measures 20 feet 9 inches at the top, 12 feet 3 inches at the bottom, and has a depth of 3 feet 6 inches. What is the area in square feet?

The cross section of a trench measures 20 feet 9 inches at the top, 12 feet 3 inches at the bottom, and has a depth of 3 feet 6 inches. What is the area in square feet?

• A. 55.25 sq. ft.
• B. 57.75 sq. ft.
• C. 60.00 sq. ft.
• D. 62.50 sq. ft.

Answer: (B)

To find the area of the cross section of the trench, we can consider it as a trapezoid, given the measurements of the top and bottom widths and the depth. The area of a trapezoid can be calculated using the formula: \[ \text{Area} = \frac{(b_1 + b_2)}{2} \times h \] where \(b_1\) is the length of the top base, \(b_2\) is the length of the bottom base, and \(h\) is the height (or depth in this case). 1. **Converting Measurements**: First, we convert all measurements to feet for consistency: - Top width: 20 feet 9 inches = 20 + \(\frac{9}{12}\) = 20.75 feet - Bottom width: 12 feet 3 inches = 12 + \(\frac{3}{12}\) = 12.25 feet - Depth: 3 feet 6 inches = 3 + \(\frac{6}{12}\) = 3.5 feet 2. **Applying the trapezoid area formula**: - Calculate the sum

To find the area of the cross section of the trench, we can consider it as a trapezoid, given the measurements of the top and bottom widths and the depth. The area of a trapezoid can be calculated using the formula:

[

\text{Area} = \frac{(b_1 + b_2)}{2} \times h

]

where (b_1) is the length of the top base, (b_2) is the length of the bottom base, and (h) is the height (or depth in this case).

1. Converting Measurements: First, we convert all measurements to feet for consistency:

• Top width: 20 feet 9 inches = 20 + (\frac{9}{12}) = 20.75 feet

• Bottom width: 12 feet 3 inches = 12 + (\frac{3}{12}) = 12.25 feet

• Depth: 3 feet 6 inches = 3 + (\frac{6}{12}) = 3.5 feet

2. Applying the trapezoid area formula:

• Calculate the sum