Perimeter of polygon

Question

Find the perimeter of the polygon with the vertices G(2, 4), H(2,−3), J(−2,−3), G(2, 4), H(2,−3), J(−2,−3),  and K(−2, 4)K(−2, 4).

The perimeter is...

Answer 1

If you plot the points on an x-y plane, you'll see that the points connect to create a rectangle with sides GH, HJ, JK, and KG.

This example (especially when plotted) is relatively straightforward, but I'll give you the strategy that you can use for all problems like this.

To find the distance between two points, you can use the formula:

d = √( (x₂ – x₁)² + (y₂ – y₁)² )

Note that it doesn't matter for this formula which point you say is (x₁, y₁) or (x₂, y₂), as long as you keep them consistent.

Let's do this for each side of this rectangle:

d_GH = √( (2 – 2)² + (-3 – 4)² ) = √( 0² + (-7)² ) = √( 49 ) = 7

d_HJ = √( (2 – -2)² + (-3 – -3)² ) = √( 4² + 0² ) = √( 16 ) = 4

d_JK = √( (-2 – -2)² + (-3 – 4)² ) = √( 0² + (-7)² ) = √( 49 ) = 7

d_KG = √( (-2 – 2)² + (4 – 4)² ) = √( (-4)² + 0² ) = √( 16 ) = 4

Now that we have all four sides of the rectangle, we just have to add them up to find the perimeter:

P_GHJK = d_GH + d_HJ + d_JK + d_KG

= 7 + 4 + 7 + 4

P_GHJK = 22