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 length of one side and then multiply it by the number of sides.
First, calculate the distance between two consecutive points to find the length of one side using the distance formula:
√((x2 - x1)^2 + (y2 - y1)^2)
Using the points (-2, -4) and (1, 0):
√((1 - (-2))^2 + (0 - (-4))^2)
= √((1 + 2)^2 + (0 + 4)^2)
= √(3^2 + 4^2)
= √(9 + 16)
= √25
= 5
So, the length of one side is 5 units.
Since the polygon is equilateral, all sides have the same length. Therefore, the perimeter of the polygon is:
Perimeter = Length of one side * Number of sides
= 5 * 8
= 40
The perimeter of the equilateral polygon is 40 units.