Answer:
[tex]\frac{\pi d^2}{8}[/tex]
Step-by-step explanation:
Semicircle is HALF of a circle. The area of a circle is given by:
[tex]\pi r^2[/tex]
So, area of semi circle is:
[tex]\frac{\pi r^2}{2}[/tex]
Where r is the radius (half of diameter).
The diameter is given as "d", so the radius is half of that, this would be:
[tex]\frac{d}{2}[/tex]
Now, substituting this into "r", we get the expression for area of the semicircle:
Area = [tex]\frac{\pi r^2}{2}=\frac{\pi (\frac{d}{2})^2}{2}=\frac{\pi (\frac{d^2}{4})}{2}=\frac{\frac{\pi d^2}{4}}{2}=\frac{\pi d^2}{8}[/tex]
This is the area.
