Final answer:
To find the perimeter of the polygon, we calculate the lengths of each side and add them together. The perimeter is 22.07.
Step-by-step explanation:
To find the perimeter of a polygon, we need to add up the lengths of all the sides. In this case, the polygon has vertices at A(0,1), B(4,4), C(7,0), D(3,-3), and E(-4,-4).
Using the distance formula, we can calculate the lengths of each side:
AB = √((4-0)^2 + (4-1)^2) = √(16 + 9) = √25 = 5
BC = √((7-4)^2 + (0-4)^2) = √(9 + 16) = √25 = 5
CD = √((3-7)^2 + (-3-0)^2) = √(16 + 9) = √25 = 5
DE = √((-4-3)^2 + (-4+3)^2) = √(49 + 1) = √50 ≈ 7.07
To find the perimeter, we add up the lengths of all the sides: 5 + 5 + 5 + 7.07 = 22.07
Rounding to the nearest hundredth, the perimeter of the polygon is 22.07.