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Find out the centroid of the shaded area:
Find out the centroid of the shaded area illustrated in Figure (a).
The shaded area A may be considered as the algebraic sum of three areas - A1, A2 and A3 as illustrated in Figure b).
A = A1 + A2 - A3
Taking the origin of axes at H we may write:
A1 = 200 × 200 = 40,000 mm2 with centroid at (100, 100),
A2 = π× 100 2 /2 = 15, 708 mm2 with centroid at (242.4, 100), and
A3 = - π × 602/2 = - 5655 mm2 with centroid at (100, 25.44).
∴ x¯ = 724/5.0053 = 144.65 mm ∴ y¯ = 543/5.0053 = 108.50 mm .
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