I have some problems finding the perimeter of the unshaded region as the picture below. $PQ = QR = PS$ is $5$ cm. $SR$ is $11$ cm. The radius of the circle is $1.2$ cm.
Perimeter of the trapezium: $5\times3 + 11 = 26$ cm
Perimeter of shaded circle: $2\times\pi\times(1.2) = 2.4\times\pi$ cm
Perimeter of unshaded region: $26 + 2.4\times\pi = 33.5 $cm
My question is why the perimeter of the shaded circle is added to the perimeter of trapezium instead of subtracting it ? I fully understand if for the area of unshaded region, the area of trapezium minus the area of circle, Why not for perimeter?
The perimeter is the boundary between a region and its complement. If a region has a hole in it, the perimeter of the hole is a boundary between the region and its complement, so that counts positively in the boundary of the region.