Question

2. What is the area of the composite figure? Show all work!

(i dont know how to insert the image so ill list the points down below)
1.(-5, -3)
2.(-5, 2)
3.(-3, 5)
4.(-1, 2)
5.(1, 5)
6.(3, 2)
7.(3, -1)

Answer 1

Area of composite figure is 44 squnits

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)

`AE=HF=\sqrt((3+5)^2+(2-2)^2)=8units`

C is the mid point as
`(-1,2)=((-5+3)/(2), (2+2)/(2))`

∴ AC=CE=4 units

`HG=\sqrt((-5+5)^2+(-3+1)^2)=2units`

`ar(ABC)=ar(CDE)=(1)/(2)* base * height`

=
`(1)/(2)* 4* 3=6squnits`

`ar(AEFH)=AE* FH=8* 3=24 squnits`

`ar(FGH)=(1)/(2)* HF * HG`

=
`(1)/(2)* 8* 2=8squnits`

Area of composite figure=ar(ABC)+ar(CDE)+ar(AEFH)+ar(FGH)

= 6+6+24+8=44 squnits