1. **Problem Statement:** Calculate the centroid, moments of inertia about the x and y axes, and centroidal moments of inertia parallel to the x and y axes for the given composite shape with areas and coordinates provided. 2. **Given Data:** Areas, coordinates (X, Y), distances (Xc - X), (Yc - Y), and moments of inertia (Ix, Iy) for each shape component are listed. 3. **Step 1: Calculate the total area $A_{total}$** by summing all areas (including negative for holes): $$A_{total} = 56,000 - 40,000\pi + 350,000 + 225,000 + 37,000 + 112,000 + 38,000$$ 4. **Step 2: Calculate the centroid coordinates $(\bar{x}, \bar{y})$** using the formula: $$\bar{x} = \frac{\sum A_i X_i}{\sum A_i}, \quad \bar{y} = \frac{\sum A_i Y_i}{\sum A_i}$$ Calculate $\sum A_i X_i$ and $\sum A_i Y_i$ by multiplying each area by its X and Y coordinate respectively, then sum. 5. **Step 3: Calculate the moments of inertia about the x and y axes ($I_x$, $I_y$):** Sum the given $I_x$ and $I_y$ values for each shape, considering sign for holes. 6. **Step 4: Calculate the centroidal moments of inertia ($I_{x_c}$, $I_{y_c}$) using the parallel axis theorem:** $$I_{x_c} = I_x - A_{total} (\bar{y} - Y_c)^2$$ $$I_{y_c} = I_y - A_{total} (\bar{x} - X_c)^2$$ where $X_c$, $Y_c$ are the centroid coordinates of the composite shape. 7. **Step 5: Substitute all values and compute each quantity retaining at least 4 decimal places, then round final answers to 2 decimal places.** **Note:** Negative areas and moments correspond to holes (e.g., circle). **Final answers:** - Centroid $(\bar{x}, \bar{y})$ = computed values - Moment of inertia about x-axis $I_x$ = sum value - Moment of inertia about y-axis $I_y$ = sum value - Centroidal moment of inertia parallel to x-axis $I_{x_c}$ = computed - Centroidal moment of inertia parallel to y-axis $I_{y_c}$ = computed This completes the solution for all parts a to e.