The figure below shows a composite area consisting of an out…
The figure below shows a composite area consisting of an outer rectangle and an inner rectangular cutout. The axes intersect at the origin (0,0). Dimensions: Outer rectangle: x = -5 to x = 5, y = 0 to y = 6 Inner cutout: x = -2 to x = 2, y = 0 to y = 2 Figure 2.jpg Determine the centroid coordinates of the shaded area. Break down your solution into steps. Fill in the blanks for each step and select the correct answer from the given options. Step 1: Compute Areas Outer rectangle area = [BLANK-1] Options: 60, 62, 64, 66, 68 Inner rectangle area = [BLANK-2] Options: 4, 6, 8, 10, 12 Step 2: Compute Centroid Coordinates of Each Rectangle x ¯ 1 = [BLANK-3] Options: 0, -1, 1, 2, -2 x ¯ 2 = [BLANK-4] Options: 0, 1, 2, -1, -2 y ¯ 1 = [BLANK-5] Options: 2.5, 3, 4, 5, 6 y ¯ 2 = [BLANK-6] Options: 0.5, 1, 1.5, 2, 2.5 Step 3: Compute Weighted Terms A 1 × x ¯ 1 = [BLANK-7] Options: 0, 60, 120, -60, -120 A 2 × x ¯ 2 = [BLANK-8] Options: 0, 8, 16, -8, -16 A 1 × y ¯ 1 = [BLANK-9] Options: 150, 180, 200, 210, 220 A 2 × y ¯ 2 = [BLANK-10] Options: 8, 10, 12, 14, 16 Step 4: Compute Totals Total Area = [BLANK-11] Options: 48, 52, 54, 56, 58 Sum of A i × x ¯ i = [BLANK-12] Options: 0, 8, 16, -8, -16 Sum of A i × y ¯ i = [BLANK-13] Options: 158, 160, 162, 164, 172 Step 5: Final Centroid Coordinates X – ≈ [BLANK-14] Options: -0.33, 0.00, 0.33, 0.50, 1.00 Y – ≈ [BLANK-15] Options: 2.52, 3.00, 3.31, 3.45, 3.63
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