Question

find the area of the shaded region in the figure. use the (pi) key for (pi). the area of the shaded region in the figure is approximately (square) (type an integer or decimal rounded to the nearest tenth as needed.)

Explanation:

Step1: Calculate area of the circle

The formula for the area of a circle is $A_{circle}=\pi r^{2}$, where the radius $r = \frac{4.2}{2}=2.1$. So $A_{circle}=\pi\times(2.1)^{2}=\pi\times4.41\approx 3.14\times4.41 = 13.8474$.

Step2: Calculate area of the square

The formula for the area of a square is $A_{square}=s^{2}$, where the side - length $s = 1.2$. So $A_{square}=(1.2)^{2}=1.44$.

Step3: Calculate area of the shaded region

The area of the shaded region $A = A_{circle}-A_{square}$. So $A=13.8474 - 1.44=12.4074\approx12.4$.

Answer:

$12.4$