To find the area, you have to find the area of 2 different shapes... because you have a rectangle that has a semicircle cut out of it, you have to first find the area of the whole rectangle, then subtract the area of the semicircle. The area of the whole rectangle would be...
A= length x width A = 12m x 8m = 96 m^2
Now we need to find the area of the semicircle. C is the midpoint of the semicircle and since the circle fits perfectly in the width of the rectangle, we know it's diameter is 8m.
The area of a circle is found with the equation A = pi (r)^2 so the area of a semicircle is found with the equation
A = pi(r)^2 / 2
Since the diameter is 8m then the radius is 8/2 = 4m
Let's plug it into the equation
A = pi(r)^2 / 2 A = 3.14(4)^2 / 2 A = 25.12m^2
Now let's subtract the area of the semicircle from the area of the rectangle and we will be left with the shaded area.
