Questions
How do you find the centroid of a composite area?
Split it into simple shapes whose centroids you know. For each part, list A, x̄ and ȳ, then A·x̄ and A·ȳ. Add the columns. X̄ = ΣA·x̄ ÷ ΣA and Ȳ = ΣA·ȳ ÷ ΣA, both measured from the same origin.
How do you handle a hole in a composite area?
Treat the hole as a part with a negative area. Its x̄ and ȳ are where its centroid is, as usual, so its A·x̄ and A·ȳ come out negative and are subtracted in the sums.
Where is the centroid of a semicircle?
On its axis of symmetry, 4r/(3π) from the diameter, about 0.424r. A quarter circle’s centroid is 4r/(3π) from each of its two straight edges.
Where is the centroid of a right triangle?
A third of each leg from the right angle: b/3 along the base and h/3 up the height. Measuring from the far end, or using half, are the usual slips.
How many figures should I give?
At least three significant figures. Areas and distances from rectangles and triangles are exact, so they can be typed in full. Round only at the end.
How do I give my class the same problems?
Press Share with class and send the link: everyone gets the same set code and shapes. Print makes up to 30 different copies, each with its own answer key.
Sources, checked 2 November 2026: Baker and Haynes, Engineering Statics: Open and Interactive, 7.5 Centroids using composite parts (holes as negative areas), Table C.1.1 Centroids of common shapes, Table C.2.1 Moments of inertia of common shapes and 10.4 Moment of inertia of composite shapes. The same formulas are on the inside covers of Hibbeler and of Beer and Johnston.