Question

What is the perimeter of this polygon? Round your answer to the nearest

tenth.
(2,3)
(-4, 0)
(0, -4)
O
A. 24.0 units
O
B. 21.6 units
O
C. 24.6 units
O
D. 23.3 units
(APEX)

Answer 1

B. 21.6 units

Step-by-step explanation:

The polygon in the picture seems to be irregular, so to find the perimeter we should try to find each length of the 4 sides. We can find the vertical distance, horizontal distance, then using the Pythagoras theorem to find the line length.

1. first side

The length from (-4, 0) to (2, 3) should be:

y= 2-(-4)= 6

x= 3-0= 3

a=
`\sqrt{3^(2)+6^(2)}`=
`√(45)`

a= 6.70

2. second side

The length from (2, 3) to (4, 0) should be:

y= 4-2= 2

x= 0-3= -3

b=
`\sqrt{2^(2)+(-3)^(2)}`=
`√(13)`

b= 3.60

3. third side

The length from (4, 0) to (0, -4) should be:

y= 0-4= -4

x= -4-0= -4

c=
`\sqrt{(-4)^(2)+4^(2)}`=
`√(32)`

c= 5.65

4. fourth side

The length from (0, -4) to (-4, 0)should be:

y= -4-0= -4

x= 0-(-4)= 4

d=
`\sqrt{(-4)^(2)+4^(2)}`=
`√(32)`

d=5.65

Perimeter = a + b + c + d

Perimeter = 6.70 + 3.60 + 5.65 + 5.65 = 21.6