Final answer:
To find the area of the vertical cross-section of the swimming pool, the area of a trapezoid formula is used. The calculation indicates an area of 48 m², which does not match any of the provided options, suggesting an error in the question or options. Therefore, the correct answer would be 'None of the above' based on the calculations done.
Step-by-step explanation:
The problem involves calculating the area of the vertical cross-section of a swimming pool that has a trapezoidal shape due to the varying depths at each end. The length of the pool is given as 30 m, with one end being 0.80 m deep and the other end 2.4 m deep. To find the area of the cross-section, we can use the formula for the area of a trapezoid, which is A = (1/2) * (a + b) * h, where 'a' and 'b' are the lengths of the parallel sides and 'h' is the distance between the parallel sides.
In this case, 'a' is the depth at the shallow end (0.80 m), 'b' is the depth at the deeper end (2.4 m), and 'h' is the length of the pool (30 m). Plugging in the values, we get:
A = (1/2) * (0.80 m + 2.4 m) * 30 m
A = (1/2) * 3.2 m * 30 m
A = 1.6 m * 30 m
A = 48 m²
However, none of the provided options match the calculated result. It is possible there has been an error in the options given or a misinterpretation of the question. Therefore, the correct answer would be 'None of the above' based on the calculations done.