According to the description in statement we prepared a representation of the figure in the image attached below. The <em>shaded</em> area is equal to the area of the <em>circle</em> sector ( $A$ ), in square centimeters:

$A = \frac{\theta\cdot \pi \cdot R^{2}}{360}$ (1)

Where:

$R$ - Length of the radius, in centimeters.
$\theta$ - Angle of circle arc, in degrees.

If we know that $\theta = 40^{\circ}$ and $R = 10\,cm$ , then the area of the circle is:

$A = \frac{(40)\cdot \pi\cdot (10\,cm)^{2}}{360}$

$A\approx 34.907\,cm^{2}$

The value of the <em>shaded</em> area is approximately 34.907 square centimeters. $\blacksquare$

To learn more on areas, we kindly invite to check this verified question: brainly.com/question/16151549

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