1 Answer

Welegan · Answer 1 · 2023-04-12T12:14:28+0000

The area of a rectangle can be calculated with this formula:

Where "l" is the length and "w" is the width.

The area of a circle can be found with this formula:

$A_c=\pi r^2$

Where "r" is the radius of the circle.

Let be "d" the diameter of the circle shown in the picture. Since it touches the rectangle at two points, you can identify that:

Since the radius of a circle is half the diameter, in this case this is:

$d=(4.2cm)/(2)=2.1\operatorname{cm}$

Therefore, the area of the circle is:

$A_c=\pi(2.1\operatorname{cm})^2=13.85\operatorname{cm}^2$

Now you must find the total area of the rectangle. Knowing that:

$\begin{gathered} l=11\operatorname{cm} \\ w=4.2\operatorname{cm} \end{gathered}$

You get:

$A_r=(11\operatorname{cm})(4.2\operatorname{cm})=46.2\operatorname{cm}^2$

In order to find the total area of the shaded region, you must subtract the total area of the rectangle and the area of the circle. Then, this is:

$A_(sr)=46.2\operatorname{cm}-13.85\operatorname{cm}=32.35\operatorname{cm}^2$

The answer is: Option D.

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