Need help finding the area of the shaded region. Round to the nearest tenth. Need help ASAP

Accepted Solution

Answer:   294.4 m²Step-by-step explanation:Separate the shaded region into two parts:The section containing the central angle of 230° (360° - 130°)The triangle with sides 11.1, 11.1 & 20.12 (use Law of Cosines)[tex]1.\ Area(A)=\pi\ r^2\ \bigg(\dfrac{\theta}{360}\bigg)\\\\\\.\qquad \qquad =\pi(11.1)^2\bigg(\dfrac{230}{360}\bigg)\\\\\\.\qquad \qquad =247.3[/tex][tex]2.\ \text{Use Law of cosines to find the length of the third side.}\\\text{ Then use Heron's formula to find the Area of the triangle.}\\\\s=\dfrac{11.1+11.1+20.12}{2}=21.16\\\\\\A=\sqrt{s(s-a)(s-b)(s-c)}\\\\.\ =\sqrt{21.16(21.16-11.1)(21.16-11.1)(21.16-20.12)}\\\\.\ =\sqrt{2227}\\\\.\ =47.1[/tex]Area of shaded region = Area of (1) + Area of (2)                                       =    247.3     +      47.1                                       =               294.4