Answer:
Option B.
Step-by-step explanation:
The given vertices of the polygon are (-6,-2),(-5,1),(-1,4),(1,1),(5,3),(1,-2).
We need to find the area of the polygon.
Plot the given vertices and on a coordinate plane and draw the polygon. Divide the polygon in 4 parts as shown below.
Area of rectangle is
[tex]A=length\times width[/tex]
Area of triangle is
[tex]A=\dfrac{1}{2}\times base\times height[/tex]
Area of each figure is
[tex]A_1=\dfrac{1}{2}\times 1\times 3=1.5[/tex]
[tex]A_2=\dfrac{1}{2}\times 6\times 3=9[/tex]
[tex]A_3=\dfrac{1}{2}\times 4\times 3=6[/tex]
[tex]A_4=6\times 3=18[/tex]
Area of polygon is
[tex]A=A_1+A_2+A_3+A_4[/tex]
[tex]A=1.5+9+6+18=34.5[/tex]
The area of polygon is 34.5 units².
Therefore, the correct option is B.
