9514 1404 393
Answer:
24.1 units
Step-by-step explanation:
This is done using the Pythagorean theorem (or distance formula) to find the lengths of the sides.
For each side of the figure (except the bottom horizontal), you need to identify the dimensions of the right triangle whose hypotenuse is the side of interest. For example, LM is the hypotenuse of a triangle 4 units high and 1 unit wide. The Pythagorean theorem tells you LM has a length of ...
LM = √(4^2 +1^2) = √17 ≈ 4.12
Similarly ...
KL = √(2^2 +2^2) = √8 ≈ 2.83
JK = √(1^2 +6^2) = √37 ≈ 6.08
NJ = √(5^2 +1^2) = √26 ≈ 5.10
Of course, the length of MN is found by finding the difference of the x-coordinates:
MN = 3 -(-3) = 6
Then the perimeter is the sum of side lengths:
4.12 +2.83 +6.08 +5.10 +6.00 = 23.17 ≈ 24.1 . . . units
