Explanation

This tests the area of a regular polygon via its apothem. Joining the centre to each vertex divides the polygon into n congruent triangles, each with base = one side and height = r (the inradius, since the inscribed circle touches every side). Each triangle's area is ½ × side × r, so the total is n × ½ × side × r = ½ × perimeter × r = pr/2. Option (a) (p+n)r has the wrong dimensions — an area must scale as length squared. Hence option (c).