Question

A semi- circle sits on top of a rectangle. Find it's area and perimeter. Use 3.14 for pi. The height is 4in and the base is 3in

Answer 1

check the picture below

if the width or base of the rectangle is 3 units, that means the diameter of the semi-circle is 3, and thus the radius is half that, notice the red radius line

the area of the figure is the area of the rectangle 3x4, plus the area of the semi-circle


`\bf \textit{area of a circle}\\\\ A=\pi r^2\\\\ -------------------------------\\\\ \textit{area of a semi-circle}\\\\ A=\cfrac{\pi r^2}{2}\qquad \begin{cases} r=radius\\ -----\\ r=(3)/(2) \end{cases}\implies A=\cfrac{\pi (3^2)/(2^2)}{2}\implies A=\cfrac{(9\pi )/(4)}{(2)/(1)} \\\\\\ A=\cfrac{9\pi }{4}\cdot \cfrac{1}{2}\implies A=\cfrac{9\pi }{8}`