Answer with explanation:
→→Using the Distance formula,
finding the distance between two points that is between two vertices
The Points which are vertices of Polygons are
1.→ A( 1, 1), B(6,13), C(8,13), D(16,-2) E(1, -2 )
![AB=\sqrt{(6-1)^2+(13-1)^2}\\\\AB=\sqrt{5^2+12^2}\\\\ AB=\sqrt{25+144}\\\\ AB=\sqrt{169}\\\\ AB=13](https://tex.z-dn.net/?f=AB%3D%5Csqrt%7B%286-1%29%5E2%2B%2813-1%29%5E2%7D%5C%5C%5C%5CAB%3D%5Csqrt%7B5%5E2%2B12%5E2%7D%5C%5C%5C%5C%20AB%3D%5Csqrt%7B25%2B144%7D%5C%5C%5C%5C%20AB%3D%5Csqrt%7B169%7D%5C%5C%5C%5C%20AB%3D13)
![BC=\sqrt{(8-6)^2+(13-13)^2}\\\\ BC=\sqrt{2^2}\\\\ BC=2](https://tex.z-dn.net/?f=BC%3D%5Csqrt%7B%288-6%29%5E2%2B%2813-13%29%5E2%7D%5C%5C%5C%5C%20BC%3D%5Csqrt%7B2%5E2%7D%5C%5C%5C%5C%20BC%3D2)
![CD=\sqrt{(16-8)^2+(-2-13)^2}\\\\ CD=\sqrt{8^2+15^2}\\\\CD=\sqrt{64+225}\\\\CD=\sqrt{289}\\\\CD=17\\\\DE=\sqrt{(16-1)^2+(-2+2)^2}\\\\DE=\sqrt{15^2}\\\\DE=15 \\\\AE=\sqrt{(1-1)^2+(-2-1)^2}\\\\ AE=\sqrt{3^2}\\\\ AE=3](https://tex.z-dn.net/?f=CD%3D%5Csqrt%7B%2816-8%29%5E2%2B%28-2-13%29%5E2%7D%5C%5C%5C%5C%20CD%3D%5Csqrt%7B8%5E2%2B15%5E2%7D%5C%5C%5C%5CCD%3D%5Csqrt%7B64%2B225%7D%5C%5C%5C%5CCD%3D%5Csqrt%7B289%7D%5C%5C%5C%5CCD%3D17%5C%5C%5C%5CDE%3D%5Csqrt%7B%2816-1%29%5E2%2B%28-2%2B2%29%5E2%7D%5C%5C%5C%5CDE%3D%5Csqrt%7B15%5E2%7D%5C%5C%5C%5CDE%3D15%20%5C%5C%5C%5CAE%3D%5Csqrt%7B%281-1%29%5E2%2B%28-2-1%29%5E2%7D%5C%5C%5C%5C%20AE%3D%5Csqrt%7B3%5E2%7D%5C%5C%5C%5C%20AE%3D3)
→→AB+BC+CD+DE+EA= 13+2+17+15+3
=50 units
2. K(4,2), L(8,2), M(12,5), N(6,5), O(4,4)
![KL=\sqrt{(8-4)^2+(2-2)^2}=\sqrt{4^2}=4\\\\ LM=\sqrt{(8-12)^2+(2-5)^2}=\sqrt{4^2+3^2}=\sqrt{5^2}=5\\\\MN=\sqrt{(12-6)^2+(5-5)^2}=\sqrt{6^2}=6\\\\NO=\sqrt{(6-4)^2+(5-4)^2}=\sqrt{2^2+1^2}=\sqrt{5}\\\\KO=\sqrt{(4-4)^2+(4-2)^2}=\sqrt{2^2}=2](https://tex.z-dn.net/?f=KL%3D%5Csqrt%7B%288-4%29%5E2%2B%282-2%29%5E2%7D%3D%5Csqrt%7B4%5E2%7D%3D4%5C%5C%5C%5C%20LM%3D%5Csqrt%7B%288-12%29%5E2%2B%282-5%29%5E2%7D%3D%5Csqrt%7B4%5E2%2B3%5E2%7D%3D%5Csqrt%7B5%5E2%7D%3D5%5C%5C%5C%5CMN%3D%5Csqrt%7B%2812-6%29%5E2%2B%285-5%29%5E2%7D%3D%5Csqrt%7B6%5E2%7D%3D6%5C%5C%5C%5CNO%3D%5Csqrt%7B%286-4%29%5E2%2B%285-4%29%5E2%7D%3D%5Csqrt%7B2%5E2%2B1%5E2%7D%3D%5Csqrt%7B5%7D%5C%5C%5C%5CKO%3D%5Csqrt%7B%284-4%29%5E2%2B%284-2%29%5E2%7D%3D%5Csqrt%7B2%5E2%7D%3D2)
→KL+LM+MN+NO+OK=4+5+6+√5+2
=17+2.24
= 19.24 units
3. F(14,-10), G(16, -10), H(19,-6), I (14,-2), J(11,-6)
![FG=\sqrt{(16-14)^2+(-10+10)^2}=\sqrt{2^2}=2\\\\ GH=\sqrt{(19-16)^2+(-6+10)^2}=\sqrt{4^2+3^2}=\sqrt{5^2}=5\\\\HI=\sqrt{(19-14)^2+(-6+2)^2}=\sqrt{5^2+4^2}=\sqrt{25+16}=\sqrt{41}\\\\IJ=\sqrt{(14-11)^2+(-2+6)^2}=\sqrt{3^2+4^2}=\sqrt{5^2}=5\\\\JF=\sqrt{(14-11)^2+(-10+6)^2}=\sqrt{3^2+4^2}=\sqrt{5^2}=5](https://tex.z-dn.net/?f=FG%3D%5Csqrt%7B%2816-14%29%5E2%2B%28-10%2B10%29%5E2%7D%3D%5Csqrt%7B2%5E2%7D%3D2%5C%5C%5C%5C%20GH%3D%5Csqrt%7B%2819-16%29%5E2%2B%28-6%2B10%29%5E2%7D%3D%5Csqrt%7B4%5E2%2B3%5E2%7D%3D%5Csqrt%7B5%5E2%7D%3D5%5C%5C%5C%5CHI%3D%5Csqrt%7B%2819-14%29%5E2%2B%28-6%2B2%29%5E2%7D%3D%5Csqrt%7B5%5E2%2B4%5E2%7D%3D%5Csqrt%7B25%2B16%7D%3D%5Csqrt%7B41%7D%5C%5C%5C%5CIJ%3D%5Csqrt%7B%2814-11%29%5E2%2B%28-2%2B6%29%5E2%7D%3D%5Csqrt%7B3%5E2%2B4%5E2%7D%3D%5Csqrt%7B5%5E2%7D%3D5%5C%5C%5C%5CJF%3D%5Csqrt%7B%2814-11%29%5E2%2B%28-10%2B6%29%5E2%7D%3D%5Csqrt%7B3%5E2%2B4%5E2%7D%3D%5Csqrt%7B5%5E2%7D%3D5)
→FG+GH+HI+IJ+JF=2+5+√41+5+5=19+6.40=25.40
4.→ P(7,2), Q (12,2), R(12,6), S(7,10), T(4,6)
![PQ=\sqrt{(12-7)^2+(2-2)^2}=\sqrt{5^2}=5\\\\ QR=\sqrt{(12-12)^2+(-6+2)^2}=\sqrt{4^2+0^2}=\sqrt{4^2}=4\\\\RS=\sqrt{(12-7)^2+(-6+10)^2}=\sqrt{5^2+4^2}=\sqrt{25+16}=\sqrt{41}\\\\ST=\sqrt{(7-4)^2+(-10+6)^2}=\sqrt{3^2+4^2}=\sqrt{5^2}=5\\\\PT=\sqrt{(7-4)^2+(-2+6)^2}=\sqrt{3^2+4^2}=\sqrt{5^2}=5](https://tex.z-dn.net/?f=PQ%3D%5Csqrt%7B%2812-7%29%5E2%2B%282-2%29%5E2%7D%3D%5Csqrt%7B5%5E2%7D%3D5%5C%5C%5C%5C%20QR%3D%5Csqrt%7B%2812-12%29%5E2%2B%28-6%2B2%29%5E2%7D%3D%5Csqrt%7B4%5E2%2B0%5E2%7D%3D%5Csqrt%7B4%5E2%7D%3D4%5C%5C%5C%5CRS%3D%5Csqrt%7B%2812-7%29%5E2%2B%28-6%2B10%29%5E2%7D%3D%5Csqrt%7B5%5E2%2B4%5E2%7D%3D%5Csqrt%7B25%2B16%7D%3D%5Csqrt%7B41%7D%5C%5C%5C%5CST%3D%5Csqrt%7B%287-4%29%5E2%2B%28-10%2B6%29%5E2%7D%3D%5Csqrt%7B3%5E2%2B4%5E2%7D%3D%5Csqrt%7B5%5E2%7D%3D5%5C%5C%5C%5CPT%3D%5Csqrt%7B%287-4%29%5E2%2B%28-2%2B6%29%5E2%7D%3D%5Csqrt%7B3%5E2%2B4%5E2%7D%3D%5Csqrt%7B5%5E2%7D%3D5)
PQ+QR+RS+ST+TP=5+4+√41+5+5
=19+6.40
= 25.40 units
5.→U(4, -1), V(12, -1), W(20,-7), X(8, -7), Y(4,-4)
![UV=\sqrt{(12-4)^2+(-1+1)^2}=\sqrt{8^2}=8\\\\ VW=\sqrt{(20-12)^2+(-7+1)^2}=\sqrt{8^2+6^2}=\sqrt{64+36}=\sqrt{100}=10\\\\WX=\sqrt{(20-8)^2+(-7+7)^2}=\sqrt{12^2+0^2}=12\\\\XY=\sqrt{(8-4)^2+(-7+4)^2}=\sqrt{3^2+4^2}=\sqrt{5^2}=5\\\\YU=\sqrt{(4-4)^2+(-4+1)^2}=\sqrt{3^2+0^2}=\sqrt{3^2}=3](https://tex.z-dn.net/?f=UV%3D%5Csqrt%7B%2812-4%29%5E2%2B%28-1%2B1%29%5E2%7D%3D%5Csqrt%7B8%5E2%7D%3D8%5C%5C%5C%5C%20VW%3D%5Csqrt%7B%2820-12%29%5E2%2B%28-7%2B1%29%5E2%7D%3D%5Csqrt%7B8%5E2%2B6%5E2%7D%3D%5Csqrt%7B64%2B36%7D%3D%5Csqrt%7B100%7D%3D10%5C%5C%5C%5CWX%3D%5Csqrt%7B%2820-8%29%5E2%2B%28-7%2B7%29%5E2%7D%3D%5Csqrt%7B12%5E2%2B0%5E2%7D%3D12%5C%5C%5C%5CXY%3D%5Csqrt%7B%288-4%29%5E2%2B%28-7%2B4%29%5E2%7D%3D%5Csqrt%7B3%5E2%2B4%5E2%7D%3D%5Csqrt%7B5%5E2%7D%3D5%5C%5C%5C%5CYU%3D%5Csqrt%7B%284-4%29%5E2%2B%28-4%2B1%29%5E2%7D%3D%5Csqrt%7B3%5E2%2B0%5E2%7D%3D%5Csqrt%7B3%5E2%7D%3D3)
UV +V W+W X+XY+YU
= 8+10+12+5+3
=38 units