To get the perimeter of the trapezoid, we will add the lengths of the 4 sides together.
So, first we will need to get the length of each side.
Base of trapezoid = 8 - 2 = 4 units
The upper edge of the trapezoid = 6 - 4 = 2 units
Now, for the two side edges, we can note that they are both equal. So, we need to get only one length (as the other would be the same). I will get the length of the left side.
Coordinates of the start point are (2,4) which represent (x1,y1)
Coordinates of the end point are (4,9) which represent (x2,y2)
To get the distance between the two points, we will use the rule attached in the image below as follows:
distance = sqrt ((4-2)^2+(9-4)^2)
distance = √29
Therefore, each of the side edges equal √29 units
From the above, we can now easily get the perimeter as follows:
perimeter = 6 + 2 + √29 + √29
perimeter = 8 + 2√29 units
Based on the above calculations, the best choice would be:
D. 8 + 2√29 units