Question

I need help with 10 please it says to find the area of each shaded sector. And round to the hundredth place

Answer 1

Given:

SR = 26 m.

To find:

The area of shaded region.

Solution:

Here, QR ~ PS. So, angle PTS = angle QTR.

So, angle PTS = 73 degrees.

To find the area of the shaded region, we have to subtract the area of unshaded region from the area of the circle.

Here, SR is the diameter and SR = 26. So, the radius of the circle is 13 m.

Since, the unshaded regions are similar to each other. So, the total area of the unshaded region is:

`\begin{gathered} A=2*(73)/(360)*(22)/(7)*(13)^2 \\ =(542828)/(2520) \\ =215.41m^2 \end{gathered}`

The area of the circle is:

`\begin{gathered} A=\pi r^2 \\ =(22)/(7)*(13)^2 \\ =(3718)/(7) \\ =531.14 \end{gathered}`

So, the area of shaded region is:

`531.14-215.41=315.73m^2`

Thus, the area of the shaded region is 315.73 m^2.