Question

I need help finding the area of the shaded sector!

Answer 1

The answe will be 11-5555555

Answer 2

The area of a sector of a circle is ½ r² ∅, where r is the radius and ∅ the angle in radians subtended by the arc at the centre of the circle. So in the below diagram, the shaded area is equal to ½ r² ∅ . We also have that

`180\text{ grados = }\pi\text{ rad }`

For thus we have that the angle 260 in radians is

`260\cdot\frac{\pi\text{ rad}}{180}=1.444\text{ }\pi\text{ rad}`

So the area of that sector is

`\begin{gathered} A\text{ = }(1)/(2)(4)^2\cdot(1.444\text{ }\pi\text{ rad)} \\ =(16)/(2)\cdot(1.444\text{ }\pi\text{ rad)} \\ =\text{ 8 }\cdot(1.444\text{ }\pi\text{ rad)} \\ =\text{ 11.5555 }\pi\text{ rad} \end{gathered}`

The answer is 11.5555 pi rad.