Question

Two consecutive vertices of a regular octagon are located at (1, 4) and (4,8). This octagon's perimeter is.....?

Answer 1

40 units

Explanation:

An octagon is a polygon with 8 sides. A regular octagon is an octagon in which all their sides and angles are equal to each other.

Since the vertices of a regular octagon are located at (1, 4) and (4,8), hence the length of the side is gotten using the formula for calculating the distance between two points
`X(x_1,y_1)\ and\ Y (x_2,y_2)`.

`|XY|=√((x_2-x_1)^2+(y_2-y_1)^2)`

Hence:

`Length=√((4-1)^2+(8-4)^2)=5\ units`

Since all the sides of a regular octagon are equal, therefore:

Perimeter = 8 × length = 8 × 5 = 40 units