Final answer:
The question involves using the method of composite areas to calculate the second moments of area (Ix and Iy) for a triangle, which is an important concept in engineering mechanics and structural analysis.
Step-by-step explanation:
The question relates to the calculation of second moments of area (also known as moments of inertia for cross-sections) of a triangle around the x-axis (Ix) and y-axis (Iy) using the method of composite areas in the field of engineering.
The method of composite areas involves decomposing complex geometries into simpler shapes whose moments of inertia are well known.
Once these simpler shapes have their moments calculated, they can be added or subtracted from each other to find the moment of inertia of the complex shape.
For example, if we're given a right triangle, we can calculate Ix and Iy by using the base (b) and height (h) of the triangle with the standard formulas Ix = (1/36)bh³ and Iy = (1/36)b³h, taking care to adhere to the parallel axis theorem if the axis of rotation doesn't coincide with the base of the triangle.