We are given a diagram and want to find the area of the shaded region. Let's take a look at the diagram.
To find the area of the shaded region, we will subtract the combined area of the circles from the area of the square. First, note that the segment that we know is 7 inches long is 2 times the length r of the radius of one of the circles.
This tells us that the radius of each of the four circles is 3.5 inches. Recall the formula for the area C of a circle with radius r.
C = π r^2
By substituting 3.5 for r in this formula, we can calculate the area of a single circle.
Now, let's calculate the area of the square. Remember that the radius of each circle is 3.5 inches.
As we can see, the length a of the side of the square is the same as the length of 4 radiuses of the circle.
a = 4r ⇒ a = 14in
The length of the side of our square is 14 inches. Now, recall the formula for the area S of a square with side length a.
S = a^2
By substituting 14 for a in this formula, we will calculate the area of the square.
Now that we know that the area S of the square is 196 and the area of a single circle C is approximately 38.48, we can calculate the area of the shaded region.
