Respuesta :

[tex]\bf \textit{area of a segment of a circle}\\\\ A=\cfrac{r^2}{2}\left( \cfrac{\pi \theta}{180}\ - \ sin(\theta) \right)\qquad \begin{cases} \theta=\textit{angle in degrees}\\ r=radius \end{cases}[/tex]
Ver imagen jdoe0001

The exact area of the shaded region of the above will be:

  • Area of sector = [tex]\frac{x}{360}[/tex] x  πr²

What is the area about?

Note that to find the Area of shaded figure, the following equation will be used:

Area of shaded figure = area of sector CBD + area of sector CAD - area of CBD - area of CAD

= 60/360  x  π  x  10² + 90/360 x  π  x  (√50)² - √3/4 x  10² - 1/2 (√50)²

= 50π/3 + 25π/2 - 50√3/2 - 50/2

= 175π - 150√3 - 150 = 6 sq/in

Therefore, the Area of sector = [tex]\frac{x}{360}[/tex] x  πr²

See full question below

Given: BC = 10 inches

AC = inches

m∠CBD = 60°

m∠CAD = 90°

Calculate the exact area of the shaded region.

Learn more about sector from

https://brainly.com/question/22972014

#SPJ6