To calculate the perimeter of each polygon defined by the coordinates given and round the result to the nearest whole number, we'll follow these steps:
1. Calculate the distance between each pair of consecutive vertices.
2. Sum these distances to get the perimeter of the polygon.
3. Round the perimeter to the nearest whole number.
### Polygon 1: [tex]\((10, 6), (11, 10), (17, 7), (12, 3)\)[/tex]
1. Calculate the distance between consecutive points:
- Between [tex]\((10, 6)\)[/tex] and [tex]\((11, 10)\)[/tex]
- Between [tex]\((11, 10)\)[/tex] and [tex]\((17, 7)\)[/tex]
- Between [tex]\((17, 7)\)[/tex] and [tex]\((12, 3)\)[/tex]
- Between [tex]\((12, 3)\)[/tex] and [tex]\((10, 6)\)[/tex]
2. Sum these distances:
- Distance from A to B
- Distance from B to C
- Distance from C to D
- Distance from D to A
After summing up these distances and rounding the result, the perimeter of the first polygon is: 21
### Polygon 2: [tex]\((9, 7), (11, 9), (15, 7), (13, 2)\)[/tex]
1. Calculate the distance between consecutive points:
- Between [tex]\((9, 7)\)[/tex] and [tex]\((11, 9)\)[/tex]
- Between [tex]\((11, 9)\)[/tex] and [tex]\((15, 7)\)[/tex]
- Between [tex]\((15, 7)\)[/tex] and [tex]\((13, 2)\)[/tex]
- Between [tex]\((13, 2)\)[/tex] and [tex]\((9, 7)\)[/tex]
2. Sum these distances:
- Distance from A to B
- Distance from B to C
- Distance from C to D
- Distance from D to A
After summing up these distances and rounding the result, the perimeter of the second polygon is: 19
### Polygon 3: [tex]\((-3, 5), (-5, 4), (1, -4), (5, -2)\)[/tex]
1. Calculate the distance between consecutive points:
- Between [tex]\((-3, 5)\)[/tex] and [tex]\((-5, 4)\)[/tex]
- Between [tex]\((-5, 4)\)[/tex] and [tex]\((1, -4)\)[/tex]
- Between [tex]\((1, -4)\)[/tex] and [tex]\((5, -2)\)[/tex]
- Between [tex]\((5, -2)\)[/tex] and [tex]\((-3, 5)\)[/tex]
2. Sum these distances:
- Distance from A to B
- Distance from B to C
- Distance from C to D
- Distance from D to A
After summing up these distances and rounding the result, the perimeter of the third polygon is: 27
Thus, the perimeters of the polygons, rounded to the nearest whole number, are:
- 21
- 19
- 27
