Question

Find the area of the shaded region. Round the nearest hundredth if necessary. YZ=14.2m

Answer 1

Complete Question

The complete question is shown on the first uploaded image

Answer:

1

   $A_1 = 67.58 \ in^2$

2

   $A_2 =415.4 \ ft^2$

3

   $A_3 = 8.48 \ cm^2$

4

  $A_4 = 480.38 \ m^2$

Step-by-step explanation:

Generally the area of a sector is mathematically represented as

         $A = \frac{\theta}{360} * \pi r^2$

Now at $r_1 = 11 in$ and  $\theta_1 = 64^o$

       $A_1 = \frac{64}{360} * 3.142 * 11^2$

       $A_1 = 67.58 \ in^2$

Now at  $r_2 = 20 ft$ in and  $\theta_2 = 119 ^o$

       $A_2 = \frac{119}{360} * 3.142 * 20^2$

       $A_2 =415.4 \ ft^2$

Now at  $r_3 = 6.5 cm$   and  $\theta_3 = 23 ^o$

     $A_3 = \frac{23}{360} * 3.142 * 6.5 ^2$

      $A_3 = 8.48 \ cm^2$

Now at  $r_4 = 14.2 m$   and  $\theta_4 = 360 -87 = 273 ^o$

         $A_4 = \frac{273}{360} * 3.142 * 14.2^2$

          $A_4 = 480.38 \ m^2$