Question

Find the area and perimeter of a semicircle on top of a rectangle 4in by 6in

Answer 1

General Idea:

The formula to find the area and perimeter of a semicircle is given below, where r is the radius of circle.

$Area \; of \; the \; semicircle = \pi r^2/2\\ \\ Perimeter\; of \; Semicircle\; =\pi r\\ \\ radius (r) = \frac{diameter}{2}$

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

$Area \; of \; the \; semicircle=\pi r^2/2=\pi \cdot (2)^2/2\\\\Area\; of\; the\; semicircle=2\pi \approx 6.28 \; in^2 \\ \\Perimeter\; of\; semicircle\; =\pi r=2\pi \\ \\ Perimeter\; of\; semicircle \approx 6.28 \; in$

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

$Area \; of \; the \; semicircle=\pi r^2/2=\pi \cdot (3)^2/2\\\\Area\; of\; the\; semicircle=9\pi/2=4.5\pi \approx 14.14 \; in^2 \\ \\Perimeter\; of\; semicircle\; =\pi r=3\pi \\ \\ Perimeter\; of\; semicircle \approx 9.42 \; in$