Answer:
perimeter = 20.9 units
Step-by-step explanation:
perimeter
perimeter = distance around two dimensional shape
= addition of all sides lengths
perimeter of the figure
= AB+BC+CD+AD
distance formula:
[tex]d = \sqrt{( x_{2} - x_{1}) {}^{2} + ( y_{2} - y_{1}) {}^{2} } [/tex]
1) distance of AB
A(-3,0) B(2,4)
x1 = -3 x2 = 2
y1 = 0 y2 = 4
(substitute the values into the distance formula)
[tex]ab = \sqrt{(2 - ( - 3)) {}^{2} + (4 - 0) {}^{2} } [/tex]
[tex]ab = \sqrt{5 {}^{2} + 4 {}^{2} } [/tex]
[tex]ab = \sqrt{41} [/tex]AB = 6.4 units
2) distance of BC
B(2,4) C(3,1)
x1 = 2 x2 = 3
y1 = 4 y2 = 1
[tex]bc = \sqrt{(3 - 2) {}^{2} + (1 - 4) {}^{2} } [/tex]
[tex]bc = \sqrt{1 {}^{2} + ( - 3) {}^{2} } [/tex]
[tex]bc = \sqrt{10} [/tex]
BC = 3.2 units
3) distance of CD
C(3,1) D(-4,-3)
x1 = 3 x2 = -4
y1 = 1 y2 = -3
[tex]cd = \sqrt{( - 4 - 3) {}^{2} + ( - 3 - 1)) {}^{2} } [/tex]
[tex]cd = \sqrt{( - 7) {}^{2} + ( - 4 ){}^{2} }[/tex]
[tex]cd = \sqrt{65} [/tex]
CD = 8.1 units
4) distance of AD
A(-3,0) D(-4,-3)
x1 = -3 x2 = -4
y1 = 0 y2 = -3
[tex]ad = \sqrt{( - 4 - ( - 3)) {}^{2} + ( - 3 - 0) {}^{2} }[/tex]
[tex]ad = \sqrt{( - 1) {}^{2} + ( - 3) {}^{2} } [/tex]
[tex]ad = \sqrt{10} [/tex]
AD = 3.2 units
perimeter of figure
= AB+BC+CD+AD
= 6.4 + 3.2 + 8.1 + 3.2
= 20.9 units
