Answer:
Area of composite figure is 44 squnits
Step-by-step explanation:
We have to find the area of the composite figure which is formed by the the vertices (-5, -3), (-5, 2), (-3, 5), (-1, 2), (1, 5), (3, 2), (3, -1)
[tex]AE=HF=\sqrt((3+5)^2+(2-2)^2)=8units[/tex]
C is the mid point as [tex](-1,2)=(\frac{-5+3}{2}, \frac{2+2}{2})[/tex]
∴ AC=CE=4 units
[tex]HG=\sqrt((-5+5)^2+(-3+1)^2)=2units[/tex]
[tex]ar(ABC)=ar(CDE)=\frac{1}{2}\times base \times height[/tex]
=[tex]\frac{1}{2}\times 4\times 3=6squnits[/tex]
[tex]ar(AEFH)=AE\times FH=8\times 3=24 squnits[/tex]
[tex]ar(FGH)=\frac{1}{2}\times HF \times HG[/tex]
=[tex]\frac{1}{2}\times 8\times 2=8squnits[/tex]
Area of composite figure=ar(ABC)+ar(CDE)+ar(AEFH)+ar(FGH)
= 6+6+24+8=44 squnits
