Answer:
The perimeter and area is 93 units and 500 sq units.
Step-by-step explanation:
Given in figure
[tex]F(-10,0) A(10,10) B(20,10) C(30,0) D(20,-10) E(10,-10) [/tex]
Figure shows that
[tex]FA=FE \\ AB=ED \\ BC=CD[/tex]
In order to find the perimeter we have to find the length of FA, AB, BC, CD, DE, FE
Distance FA
[tex]FA= \sqrt{ (y2-y1)^{2} +(x2-x1)^{2} } \\ FA= \sqrt{(10-0)^{2} +(10+10)^{2} [/tex]
[tex]FA= \sqrt{500} \\ FA=22.36 units[/tex]
Distance AB
[tex]AB=20-10=10 units[/tex]
Distance BC
[tex]BC= \sqrt{ (y2-y1)^{2} +(x2-x1)^{2} }[/tex]
[tex]BC= \sqrt{ (0-10)^{2} +(30-20)^{2} }[/tex]
[tex]BC= \sqrt{200}=14.14 units [/tex]
Perimeter is equal to sum of all the sides of polygon
[tex]P=2(FA+AB+BC) \\ P=2(22.36+10+14.14)=93 units[/tex]
Now, we have to find the area
The area is equal to
=ar(ΔAFE)+ar(ABDE)+ar(ΔBDC)
area of triangle AFE
[tex]ar(AFE)=\frac{1}{2}\times 20\times 20=200 units^{2} [/tex]
area of rectangle ABDE
[tex]ar(ABDE)=10\times 20=200 units^{2} [/tex]
area of the triangle BDC
[tex]A3=\frac{1}{2}\times 20\times 10=100 units^{2} [/tex]
[tex]Areal=200+200+100=500 units^{2} [/tex]
