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 - 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).

Table

∴ x¯ = 724/5.0053         = 144.65 mm                           ∴ y¯ = 543/5.0053       = 108.50 mm .