Question

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

Answer 1

Answer:

Thus, the perimeter of the regular pentagon is 25 units

Step-by-step 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:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Using the points of the vertices:

$a=\sqrt{(3+1)^2+(-1-2)^2}$

$a=\sqrt{4^2+(-3)^2}$

$a=\sqrt{16+9}$

$a=\sqrt{25}$

a = 5

Now we calculate:

P=5a=5*5=25

Thus, the perimeter of the regular pentagon is 25 units