Question

What is the perimeter of a regular pentagon with 2 consecutive vertices at (-1,2) and (3,-1)?

Answer 1

Thus, the perimeter of the regular pentagon is 25 units

Explanation:

The perimeter of a regular pentagon of side length a is:

P = 5a

We know 2 consecutive vertices of a pentagon are the points (-1,2) and (3,-1). If we calculate the distance between them we'd have the value of a.

Given two points A(x1,y1) and B(x2,y2), the distance between them is:

`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

Using the points of the vertices:

`a=√((3+1)^2+(-1-2)^2)`

`a=√(4^2+(-3)^2)`

`a=√(16+9)`

`a=√(25)`

a = 5

Now we calculate:

P=5a=5*5=25

Thus, the perimeter of the regular pentagon is 25 units