Question

Match the polygons formed by the sets of points with their perimeters ( rounded to the nearest hundredth). Please Help me I don't understand this question. Thank you

A( 1, 1), B(6,13), C(8,13), D(16,-2) E(1, -2 )
38 units
K(4,2), L(8,2), M(12,5), N(6,5), O(4,4)
50 units
F(14,-10), G(16, -10), H(19,-6), I (14,-2), J(11,-6)
25.4 units
P(7,2), Q (12,2), R(12,6), S(7,10), T(4,6)
19.24 units
U(4, -1), V(12, -1), W(20,-7), X(8, -7), Y(4,-4)

Answer 1

38 units-U(4, -1), V(12, -1), W(20,-7), X(8, -7), Y(4,-4)

25.4 units-P(7,2), Q (12,2), R(12,6), S(7,10), T(4,6)

50 units-A( 1, 1), B(6,13), C(8,13), D(16,-2) E(1, -2 )

19.24 units-K(4,2), L(8,2), M(12,5), N(6,5), O(4,4)

Answer 2

Answer with explanation:

→→Using the Distance formula,
`\sqrt{(x_(2)-x_(1))^2+(y_(2)-y_(1))^2` 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=√((6-1)^2+(13-1)^2)\\\\AB=√(5^2+12^2)\\\\ AB=√(25+144)\\\\ AB=√(169)\\\\ AB=13`

`BC=√((8-6)^2+(13-13)^2)\\\\ BC=√(2^2)\\\\ BC=2`

`CD=√((16-8)^2+(-2-13)^2)\\\\ CD=√(8^2+15^2)\\\\CD=√(64+225)\\\\CD=√(289)\\\\CD=17\\\\DE=√((16-1)^2+(-2+2)^2)\\\\DE=√(15^2)\\\\DE=15 \\\\AE=√((1-1)^2+(-2-1)^2)\\\\ AE=√(3^2)\\\\ AE=3`

→→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=√((8-4)^2+(2-2)^2)=√(4^2)=4\\\\ LM=√((8-12)^2+(2-5)^2)=√(4^2+3^2)=√(5^2)=5\\\\MN=√((12-6)^2+(5-5)^2)=√(6^2)=6\\\\NO=√((6-4)^2+(5-4)^2)=√(2^2+1^2)=√(5)\\\\KO=√((4-4)^2+(4-2)^2)=√(2^2)=2`

→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=√((16-14)^2+(-10+10)^2)=√(2^2)=2\\\\ GH=√((19-16)^2+(-6+10)^2)=√(4^2+3^2)=√(5^2)=5\\\\HI=√((19-14)^2+(-6+2)^2)=√(5^2+4^2)=√(25+16)=√(41)\\\\IJ=√((14-11)^2+(-2+6)^2)=√(3^2+4^2)=√(5^2)=5\\\\JF=√((14-11)^2+(-10+6)^2)=√(3^2+4^2)=√(5^2)=5`

→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=√((12-7)^2+(2-2)^2)=√(5^2)=5\\\\ QR=√((12-12)^2+(-6+2)^2)=√(4^2+0^2)=√(4^2)=4\\\\RS=√((12-7)^2+(-6+10)^2)=√(5^2+4^2)=√(25+16)=√(41)\\\\ST=√((7-4)^2+(-10+6)^2)=√(3^2+4^2)=√(5^2)=5\\\\PT=√((7-4)^2+(-2+6)^2)=√(3^2+4^2)=√(5^2)=5`

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=√((12-4)^2+(-1+1)^2)=√(8^2)=8\\\\ VW=√((20-12)^2+(-7+1)^2)=√(8^2+6^2)=√(64+36)=√(100)=10\\\\WX=√((20-8)^2+(-7+7)^2)=√(12^2+0^2)=12\\\\XY=√((8-4)^2+(-7+4)^2)=√(3^2+4^2)=√(5^2)=5\\\\YU=√((4-4)^2+(-4+1)^2)=√(3^2+0^2)=√(3^2)=3`

UV +V W+W X+XY+YU

= 8+10+12+5+3

=38 units