Question

Jamie needs to build a fence around his garden, as illustrated by polygon ABCDEF on the coordinate grid below. If each unit represents one yard, what is the total length of Jamie's fence in yards?

Answer 1

Step-by-step explanation:

The complete question is shown below.

The length between two points (
`x_1,y_1`) and (
`x_2,y_2`) is:

`Length=√((y_2-y_1)^2+(x_2-x_1)^2)`

From the image attached we can get the polygon points as:

A(-5, 5), B(0. 5), C(4,2), D(1, -2), E(-2, -2), F(-5, 2). Hence the length of the polygon is gotten as:

`|AB|=√((0-(-5))^2+(5-5)^2)=5\ yards \\\\|BC|=√((4-0)^2+(2-5)^2)=5\ yards \\\\|CD|=√((1-4)^2+(-2-2)^2)=5\ yards \\\\|DE|=√((-2-1)^2+(-2-(-2))^2)=3\ yards\\ \\|EF|=√((-5-(-2))^2+(2-(-2))^2)=5\ yards \\\\|FA|=√((-5-(-5))^2+(2-5)^2)=3\ yards`

The perimeter of the fence is the sum of all the sides of the polygon = 5 + 5 + 5 + 3 + 5 + 3 = 26 yards