Question

The coordinates of the vertices of a polygon are (−2,−2), (3,−3), (4,−6), (1,−6), and (−2,−4). What is the perimeter of the polygon to the nearest tenth of a unit? 15.3 units 16.9 units 17.5 units 17.9 units

Answer 1

`color(blue)(16.9 " units to nearest tenth")`.

Explanation:

First label the points:

`A=(-2,-2), B=(3,-3), C=(4,-6)`

`D=(1,-6), E=(-2,-4)`

So we have sides:

`AB ,BC, CD, DE, EA`

To find the length of the sides, we use the distance formula:

`|d|=sqrt((x_2-x_1)^2+(y_2-y_1)^2)`

For `AB`

`|AB|=sqrt((3-(-2))^2+(-3-(-2))^2)=sqrt(26)`

For `BC`

`|BC|=sqrt((4-3)^2+(-6-(-3))^2)=sqrt(10)`

For `CD`

`|CD|=sqrt((1-4)^2+(-6-(-6))^2)=sqrt(9)=3`

For `DE`

`|DE|=sqrt((-2-1)^2+(-4-(-6))^2)=sqrt(13)`

For `EA`

`|EA|=sqrt((-2-(-2))^2+(-4-(-2))^2)=sqrt(40)=2`

The perimeter is the sum of the lengths of the sides.

`"Perimeter"=AB +BC+ CD+ DE+ EA`

`=sqrt(26)+sqrt(10)+3+sqrt(13)+2=16.86684844`

`16.9 " units"` to nearest tenth.

PLOT: