Answer:
Polygon ABCDE = 50 units
Polygon FGHIJ = 23.4 units
Polygon KLMNO = 19.24 units
Polygon UVWXY = 38 units
Step-by-step explanation:
In order to find the perimeter, we have to find lengths of all sides of given points
The distance formula will be used to find the lengths
where (x_1,y_1) are coordinates of first point and (x_2,y_2) are coordinates of second point)
So,
For A(1,1), B(6,13), C(8,13), D(16,-2) and E(1, -2)
AB = 13 units
BC = 2 units
CD = 17 units
DE = 15 units
EA = 3 units
Perimeter of polygon ABCDE = 13+2+17+15+3 = 50 units
For F(14,-10), G(16,-10), H(19,-6), I(14,-2) and J(11,-6)
FG = 2 units
GH = 5 units
HI = 6.40 units
IJ = 5 units
JF = 5 units
Perimeter of polygon FGHIJ = 2+5+6.40+5+5 = 23.4 units
For K(4,2), L(8,2), M(12,5), N(6,5) and O(4,4)
KL = 4 units
LM = 5 units
MN = 6 units
NO = 2.24 units
OK = 2 units
Perimeter of polygon KLMNO = 4+5+6+2.24+2 = 19.24 units
For P(7,2), Q(12,2), R(12,6), S(7,10) and T(4,6)
PQ= 5 units
QR= 4 units
RS=6.40 units
ST= 5 units
TP = 5 units
Perimeter of polygon PQRST = 5+4+6.40+5+5 = 25.40 units
For U(4,-1), V(12, -1), W(20,-7), X(8, -7) and Y(4,-4)
UV = 8 units
VW = 10 units
WX = 12 units
XY = 5 units
YU = 3 units
Perimeter of polygon UVWXY = 8+10+12+5+3 = 38 units