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A semicircle is half a disc, so its area is πr²/2. Its boundary is the half-circumference πr plus the straight diameter 2r, and its centroid sits 4r/(3π) above the diameter.
Area
A = πr² / 2
Perimeter
P = πr + 2r
Centroid
ȳ = 4r / (3π)
No. Half the circumference is only the curved part; you must add the diameter that closes the shape.
On the axis of symmetry, 4r/(3π) ≈ 0.4244r above the flat edge — not at r/2.