Answer:
Perimeter of polygon 1: √17 + √45 + √41 + √13,
Perimeter of polygon 2: 2√2 + √20 + √29 + √41,
Perimeter of polygon 3: √5 + √40 + √20 + √113
Explanation:
To calculate the perimeter of each polygon defined by the set of coordinates, we can use the distance formula to find the length of each side and then sum up all the side lengths.
Let's calculate the perimeter for each polygon:
Polygon with coordinates (10, 6), (11, 10), (17, 7), and (12, 3):
Length of side 1: √((11-10)^2 + (10-6)^2) = √(1^2 + 4^2) = √17
Length of side 2: √((17-11)^2 + (7-10)^2) = √(6^2 + 3^2) = √45
Length of side 3: √((12-17)^2 + (3-7)^2) = √(5^2 + 4^2) = √41
Length of side 4: √((10-12)^2 + (6-3)^2) = √(2^2 + 3^2) = √13
Perimeter = √17 + √45 + √41 + √13
Polygon with coordinates (9, 7), (11, 9), (15, 7), and (13, 2):
Length of side 1: √((11-9)^2 + (9-7)^2) = √(2^2 + 2^2) = 2√2
Length of side 2: √((15-11)^2 + (7-9)^2) = √(4^2 + 2^2) = √20
Length of side 3: √((13-15)^2 + (2-7)^2) = √(2^2 + 5^2) = √29
Length of side 4: √((9-13)^2 + (7-2)^2) = √(4^2 + 5^2) = √41
Perimeter = 2√2 + √20 + √29 + √41
Polygon with coordinates (-3, 5), (-5, 4), (1, -4), and (5, -2):
Length of side 1: √((-5+3)^2 + (4-5)^2) = √(2^2 + 1^2) = √5
Length of side 2: √((1+5)^2 + (-4+2)^2) = √(6^2 + 2^2) = √40
Length of side 3: √((5-1)^2 + (-2+4)^2) = √(4^2 + 2^2) = √20
Length of side 4: √((-3-5)^2 + (5+2)^2) = √(8^2 + 7^2) = √113
Perimeter = √5 + √40 + √20 + √113
Thus,
The perimeters of the given polygons are given above.