Question

Polygon ABCDE is shown on the coordinate grid. What is the perimeter to the nearest hundredth of a unit, of polygon ABCDE?

Answer 1

For this case we can find the distance

AB= 4

ED= 4

We can use the distance point given by:

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

Now we need to find the distance AE, we have y2= 2, y1= -3 , x2= -3, x1 = -4 and we got:

`AE=\sqrt[]{(2+3)^2+(-3+4)^2}=\sqrt[]{26}`

Similarly we can find BC and DC.

For BC we have we have y2= 2, y1= -1 , x2= 1, x1 = -1

And for DC we have y2= -1, y1= -3 , x2= 3, x1 = 0

`BC=\sqrt[]{(2+1)^2+(1+1)^2}=\sqrt[]{13}`
`DC=\sqrt[]{(-1+3)^2+(3-0)^2}=\sqrt[]{13}`

Then the perimeter is given by:

`4+4+\sqrt[]{26}+\sqrt[]{13}+\sqrt[]{13}=20.31`