polygons on the coordinate plane find perimeter

Question

find the perimeter of the polygons formed when these points are connected (1,6) (1,4) (8,4) (8,6)

Answer 1

It helps to plot the points and connect them

then you can see the points are vertices of a rectangle

with opposite sides equal, and with 4 right angles

from (1,4 to (1,6) = 2 = the difference in y coordinates, 6-4=2

from (1,4) to (8,4) = 7 = the difference in x coordinates, 8-1 =7

2 and 7 are the Width and Length of the rectangle

the perimeter = 2(W+L) = 2(2+7) = 2(9) = 18

You could also connect 3 of the points to construct 4 different triangles, each with half the area of the rectangle. The rectangle has area = 2(7) =14. Each triangle has area = 7.

they have sides 2,7 and hypotenuse sqr(2^2+7^2) =sqr53

the triangles' perimeter = 9+sqr53= about 16.28