A polygon is said to be equilateral if all of its sides are the same length. Find the perimeter of the equilateral polygon whose vertices are as follows.
(−2,−4), (1,0), (1,5), (−2,9), (−7,9), (−10,5), (−10,0), (−7,−4)
(1 point)
units
To find the perimeter of the equilateral polygon, we need to find the distance between each pair of consecutive vertices and then add them all up.
The distance between two points (x1, y1) and (x2, y2) is given by the distance formula:
d = √((x2-x1)^2 + (y2-y1)^2)
Using this formula, we can find the distance between each pair of consecutive vertices, starting with the first and second points:
d1 = √((1 - (-2))^2 + (0 - (-4))^2) = √((3^2) + (4^2)) = √(9 + 16) = √25 = 5
Continuing, we find the distances between the other consecutive pairs of vertices:
d2 = √((1 - 1)^2 + (5 - 0)^2) = √((0^2) + (5^2)) = √25 = 5
d3 = √((−2 - 1)^2 + (9 - 5)^2) = √(((-3)^2) + (4^2)) = √(9 + 16) = √25 = 5
d4 = √((−7 - (−2))^2 + (9 - 9)^2) = √(((-5)^2) + (0^2)) = √(25) = 5
d5 = √((−10 - (−7))^2 + (5 - 9)^2) = √(((-3)^2) + (-4^2)) = √(9 + 16) = √25 = 5
d6 = √((−10 - (−10))^2 + (0 - 5)^2) = √((0^2) + (-5^2)) = √25 = 5
d7 = √((−7 - (−10))^2 + ((−4) - 0)^2) = √((3^2) + (-4^2)) = √(9 + 16) = √25 = 5
Now we can add up all the distances to find the perimeter:
Perimeter = d1 + d2 + d3 + d4 + d5 + d6 + d7
= 5 + 5 + 5 + 5 + 5 + 5 + 5
= 35
Therefore, the perimeter of the equilateral polygon is 35 units.