The value of the shaded area is approximately 34.907 square centimeters.
How to calculate the area between a rhombus and a circle
According to the description in statement we prepared a representation of the figure in the image attached below. The shaded area is equal to the area of the circle sector ([tex]A[/tex]), in square centimeters:
[tex]A = \frac{\theta\cdot \pi \cdot R^{2}}{360}[/tex] (1)
Where:
- [tex]R[/tex] - Length of the radius, in centimeters.
- [tex]\theta[/tex] - Angle of circle arc, in degrees.
If we know that [tex]\theta = 40^{\circ}[/tex] and [tex]R = 10\,cm[/tex], then the area of the circle is:
[tex]A = \frac{(40)\cdot \pi\cdot (10\,cm)^{2}}{360}[/tex]
[tex]A\approx 34.907\,cm^{2}[/tex]
The value of the shaded area is approximately 34.907 square centimeters. [tex]\blacksquare[/tex]
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