Answer:
First, while this can be solved by calculating each individual area, let's do it in a smarter way.
Notice that there are two outer parts shaded, and two inner parts shaded.
When we add all of those, we get half of the larger circle.
So we only need to calculate the area of the larger circle and then divide it by two.
Remember that the area of a circle is:
A = pi*r^2
where:
pi = 3.1416
r = radius of the circle.
In the image, we can see that the diameter of the larger circle is 8ft.
And we know that r is half of the diameter, then:
r = 8ft/2 = 4ft
Now we can replace those values in the area of the larger circle and get:
A = 3.1416*(4ft)^2 = 50.27 ft^2
Half of that is:
A/2 = 21.14 ft^2.
That is the area of the shaded regions.
