Answer:
34.6
Explanation:
The perimeter of a plane geometric figure is the sum of its side lengths. This figure has two horizontal sides, so their length is easy to compute. It also has two diagonal sides, so the distance formula or Pythagorean theorem must be invoked to find their length.
The length of diagonal AC is ...
d = √((x2 -x1)² +(y2 -y1)²)
d = √((1 -6)² +(-5 -4)²) = √((-5)² +(-9)²) = √106 ≈ 10.3
The length of each horizontal segment can be found by counting grid squares or by finding the difference of x-coordinates.
AB = 6 -(-1) = 6 +1 = 7
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Two sides have length 10.3 and two sides have length 7, so the perimeter is ...
P = 2(10.3 +7) = 34.6 . . . units