Final answer:
To calculate the area between curves, specific equations or descriptions of the curves are required. The question refers to a right triangle under a curve, but without additional information or values for the base and height, the exact area cannot be determined. Generally, for a right triangle, the area is found by multiplying 1/2 times the base times the height.
Step-by-step explanation:
To solve the mathematical problem completely and find the area between the given curves, we must have the equations of the curves or a clear description of them. However, since the question does not provide explicit functions or curves but mentions the area under the curve being a right triangle, we will assume we are working with a right triangle under a linear curve.
For a right triangle, the area (A) can be calculated by multiplying 1/2 times the base (b) times the height (h). If we refer to the mentioned Figure 10.13, and assuming the time spans from 2.5 to 5 seconds as the base of the triangle, we have a base length of (5 - 2.5) = 2.5 seconds. If we know the corresponding value of the other variable (which could be velocity, for instance) at time 5 seconds, we could calculate the height and subsequently the area. Unfortunately, without specific values, the exact area cannot be calculated.
In the context of physics or engineering problems, it's common to find areas under curves in graphs that represent physical quantities over time. Without the additional information, solving this specific exercise to a definitive answer, such as mentioning the correct option answer in the final answer, is not possible.
For example, if you had a graph of velocity versus time and the values on the graph indicated a straight line forming a right triangle, you would calculate the area as I described. Given that the question lacks such concrete data, we can only speak in hypothetical terms. Therefore, this response outlines the general approach one would take but does not provide a number that can be matched to options A, B, C, or D listed in the question.