Find out the centroid of the shaded area:
Find out the centroid of the shaded area illustrated in Figure (a).
Solution
The shaded area A may be considered as the algebraic sum of three areas - A_{1}, A_{2} and A_{3} as illustrated in Figure b).
A = A_{1} + A_{2 } - A_{3}
Taking the origin of axes at H we may write:
A_{1} = 200 × 200 = 40,000 mm^{2} with centroid at (100, 100),
A_{2} = π× 100 ^{2 }/2 = 15, 708 mm^{2} with centroid at (242.4, 100), and
A_{3} = - π × 60^{2}/2 = - 5655 mm^{2} with centroid at (100, 25.44).
Table
∴ x¯ = 724/5.0053 = 144.65 mm ∴ y¯ = 543/5.0053 = 108.50 mm .