Answer:
23.22 in²
Explanation:
The area of the shaded region can be calculated as the area of the rectangle less the area of the three circles.
If the diameter of the circles is 6", the width of the rectangle is also 6" and the length of the rectangle is 3 times 6" or 18"
Then, the area of the rectangle is equal to:
Area Rectangle = Length x width
Area Rectangle = 18 in x 6 in
Area Rectangle = 108 in²
On the other hand, the area of a circle can be calculated as:
Area Circle = π·r²
Where r is the radius of the circle and π is approximately 3.14.
The radius is equal to half the diameter, so the radius is:
r = Diameter/2 = 6 in/2 = 3 in
So, the area of the circle is equal to:
Area Circle = 3.14·(3 in)²
Area Circle = 3.14 (9 in²)
Area Circle = 28.26 in²
Finally, the area of the shaded region is equal to:
Area Shaded Region = 108 in² - 3(28.26 in²)
Area Shaded Region = 108 in² - 84.78 in²
Area Shaded Region = 23.22 in²
So, the answer is 23.22 in²