Question

ABCD is a Rhombus with side length 10 cm. Angle ADC = 40. DAC is a sector of a circle with center D. BAC is a sector of a circle with center B. Calculate the shaded area.

Answer 1

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 ($A$), 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 shaded area is approximately 34.907 square centimeters. $\blacksquare$

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