Final answer:
The perimeter of triangle ADEF with the given vertices D(3, 2), E(6, 2), and F(3, -2) is calculated by adding the lengths of sides DE, DF, and EF, which are 3, 4, and 4 units respectively, resulting in a total perimeter of 11 units.
Step-by-step explanation:
To find the perimeter of triangle ADEF with vertices D(3, 2), E(6, 2), and F(3, -2), we need to calculate the distances between each pair of vertices (sides of the triangle) and then add them together. The side DE is horizontal and F lies vertically below D; these positions allow us to calculate the length of sides DE and DF directly. Then, we can use the distance formula or Pythagorean theorem to find the length of side EF.
Since points D and E have the same y-coordinate, the length of DE is simply the difference in their x-coordinates: DE = 6 - 3 = 3 units.
Because points D and F have the same x-coordinate, the length of DF is the difference in their y-coordinates: DF = 2 - (-2) = 4 units.
For side EF, this is a vertical line segment, and thus its length is also the difference in y-coordinates: EF = 2 - (-2) = 4 units.
Adding the lengths of DE, DF, and EF, we get the perimeter of triangle ADEF: Perimeter = DE + DF + EF = 3 + 4 + 4 = 11 units.