Segment AB measures 4 cm and is a diameter of circle P. In triangle ABC, point C is on circle and BC = 1 cm. What is the area of the shaded region?

Inscribed triangle ABC is a right triangle since its base is on a diameter

AC = sqrt ( 4^2 - 1^2 ) = sqrt (15)

Area of ABC =(1/2) (1) (sqrt (15)) = sqrt (15)/2

Area of circle = pi r^2 = pi * 2^2 = 4pi

Shaded area = [4pi - sqrt (15)/2 ] cm^2