General Idea:
The formula to find the area and perimeter of a semicircle is given below, where r is the radius of circle.
[tex] Area \; of \; the \; semicircle = \pi r^2/2\\ \\ Perimeter\; of \; Semicircle\; =\pi r\\ \\ radius (r) = \frac{diameter}{2} [/tex]
Applying the concept:
There are two cases for drawing a semicircle in a rectangle of the given dimension as shown in the attachment.
CASE 1: If the semicircle is drawn on top of the width of rectangle.
Then Diameter = 4 inches & Radius = 2 inches
[tex] Area \; of \; the \; semicircle=\pi r^2/2=\pi \cdot (2)^2/2\\\\Area\; of\; the\; semicircle=2\pi \approx 6.28 \; in^2 \\ \\Perimeter\; of\; semicircle\; =\pi r=2\pi \\ \\ Perimeter\; of\; semicircle \approx 6.28 \; in [/tex]
CASE 2: If the semicircle is drawn on top of the length of the rectangle of the given dimension as shown in the attachment.
Then the Diameter = 6 inches and Radius = 3 inches
[tex] Area \; of \; the \; semicircle=\pi r^2/2=\pi \cdot (3)^2/2\\\\Area\; of\; the\; semicircle=9\pi/2=4.5\pi \approx 14.14 \; in^2 \\ \\Perimeter\; of\; semicircle\; =\pi r=3\pi \\ \\ Perimeter\; of\; semicircle \approx 9.42 \; in [/tex]
