Topic Details (Notes format)

How to Calculate the Perimeter of a Semicircle

Subject: Mathematics

Book: Maths Mastery

A semicircle is half a circle, but its perimeter (also called its “circumference” boundary) includes the diameter and half the circle’s circumference. The formula is P = πr + 2r if using r for the radius, or P = (πd / 2) + d if using d for the diameter. For instance, a semicircle with radius 5 has perimeter π × 5 + 2 × 5 = 5π + 10. This knowledge helps in designing curved edges for arcs, gates, or semicircular frames. Understanding partial circle perimeters extends to advanced shapes and real-world designs with circular segments.

Practice Questions

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If sin(A) = 3/5 and cos(B) = 5/13, where A and B are acute angles, what is sin(A+B)?

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