Find the perimeter of a polygon with the following vertices
(−12, −8), (−12,7), (0,16), (12,7), (12, −8), (0, −17)
(1 point)
Responses
99
99
114
114
90
90
78
To find the perimeter of a polygon, we need to calculate the distance between each pair of consecutive vertices and then sum them up.
The distance between two points (x1, y1) and (x2, y2) is given by the formula:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Using this formula, we can find the distances between the vertices:
Distance between (-12, -8) and (-12, 7):
= √((-12 - (-12))^2 + (7 - (-8))^2)
= √(0^2 + 15^2)
= √(225)
= 15
Distance between (-12, 7) and (0, 16):
= √((0 - (-12))^2 + (16 - 7)^2)
= √(12^2 + 9^2)
= √(144 + 81)
= √(225)
= 15
Distance between (0, 16) and (12, 7):
= √((12- 0)^2 + (7 - 16)^2)
= √(12^2 + (-9)^2)
= √(144 + 81)
= √(225)
= 15
Distance between (12, 7) and (12, -8):
= √((12 - 12)^2 + (-8 - 7)^2)
= √(0^2 + (-15)^2)
= √(225)
= 15
Distance between (12, -8) and (0, -17):
= √((0 - 12)^2 + (-17 - (-8))^2)
= √((-12)^2 + (-9)^2)
= √(144 + 81)
= √(225)
= 15
Distance between (0, -17) and (-12, -8):
= √((-12 - 0)^2 + (-8 - (-17))^2)
= √((-12)^2 + 9^2)
= √(144 + 81)
= √(225)
= 15
Now, summing up all the distances:
15 + 15 + 15 + 15 + 15 + 15 = 90
Therefore, the perimeter of the polygon is 90. Answer: 90.