Let's analyze the problem step-by-step: ### Step 1 Understand the figure the coordinate axes- The image shows a symmetric structure with respect to the x-axis and y-axis. - The structure appears to be a combination of rectangles with their centers aligned along the axes. ### Step : Identify the key points and dimensions- The question asks for moment of inertia about the **x** and **y-axis**. - To the moments of inertia, we need geometry's dimensions the location of the centroid (which appears to be at the origin, given the symmetry). ### Step 3: Break the figure into parts - The structure can be divided into rectangles. - Each rectangle's dimensions and position relative to the axes are essential. ### Step 4: Use the parallel axis theorem - Moments of inertia for composite shapes are calculated by summing the moments of inertia of individual parts about the axes, considering their distances from the centroid if needed. ### Step 5: Calculation outline - For each rectangle: - Calculate its moment of inertia about its own centroid (using standard formulas: \( I = \frac{1}{12} \times \text{base} \times \text{height}^3 \) for the axis parallel to the base). - Use the parallel axis theorem if the rectangle's centroid is not on the axis of interest: \[ I_{total} = I_{centroid} + A \times d^2 \] where \(A\) is the area, and \(d\) is the distance from the rectangle's centroid to the axis. ### Step 6: Final calculation - Sum the moments of inertia of all rectangles about the x-axis to find \( I_x \). - Sum the moments of inertia about the y-axis to find \( I_y \). --- ### Final Answer: The detailed numerical answer depends on the actual dimensions which are not specified here. If dimensions are provided, you can apply the above steps systematically to compute the moments of inertia about the x and y axes.