Question

1. determine the area of the shaded region. use 3 for π. there is a square with side length 12 in, and four circles inside it. the radius of each circle is marked as 3 (presumably 3 in). the shaded regions are the areas of the square not covered by the circles.

Explanation:

Step1: Find area of square

The square has side length 12 in. The area of a square is $side^2$, so the area of the square is $12^2 = 144$ square inches.

Step2: Find radius of each circle

From the diagram, we can see that two circles fit along the side of the square (since there are two circles per row and column). The side length of the square is 12 in, so the diameter of each circle is $\frac{12}{2}=6$ in. Therefore, the radius $r$ of each circle is $\frac{6}{2}=3$ in.

Step3: Find area of one circle

The formula for the area of a circle is $A = \pi r^2$. We are given to use $\pi = 3$ and $r = 3$ in. So the area of one circle is $3\times3^2=3\times9 = 27$ square inches.

Step4: Find total area of four circles

There are four circles, so the total area of the four circles is $4\times27 = 108$ square inches.

Step5: Find area of shaded region

The area of the shaded region is the area of the square minus the total area of the four circles. So it is $144 - 108 = 36$ square inches.

Answer:

36 square inches