Final answer:
To find the approximate perimeter of the trapezoid, calculate the distance between each pair of adjacent vertices and sum the lengths of all four sides, approximating the perimeter to 36.25 units.
Step-by-step explanation:
The student is asking for the approximate perimeter of a trapezoid with given vertices. To find the perimeter, we can calculate the distance between each pair of adjacent vertices using the distance formula √((x2-x1)² + (y2-y1)²). Once we have the lengths of all four sides, we sum them up to get the perimeter.
The distances between adjacent vertices are as follows:
- Between (–6, –3) and (–2, 5) is √((–2 + 6)² + (5 + 3)²) = √(64 + 64) = √128 ≈ 11.31 units
- Between (–2, 5) and (2, 5) is √((2 + 2)² + (5 - 5)²) = √(16 + 0) = 4 units
- Between (2, 5) and (6, –3) is √((6 - 2)² + (–3 - 5)²) = √(16 + 64) = √80 ≈ 8.94 units
- Between (6, –3) and (–6, –3) is √((–6 - 6)² + (–3 + 3)²) = √(144 + 0) = 12 units
Adding these distances together, we get an approximate perimeter of the trapezoid 11.31 + 4 + 8.94 + 12 = 36.25 units.