To find the perimeter of the trapezoid, we need to know the lengths of all sides.
Given that the trapezoid is isosceles, the non-parallel sides (legs) are congruent. Let's denote the length of each leg as \( l \).
Now, we can use the properties of the trapezoid to find the length of the legs.
Since the upper base has length 16 and the altitude is 6√3, we can use these values to find the length of each leg using the right triangle formed by the altitude, one leg, and half the difference in base lengths:
l² = (16/2)^2 + 6\sqrt{3})^2
l^2 = 64 + 108
l^2 = 172
l = sqrt{172}
l = 2\sqrt{43}
Now, we can find the perimeter:
p = 16 + 16 + 2(2\sqrt{43}) \]
p = 32 + 4\sqrt{43}
Therefore, the perimeter of the trapezoid is
(32 + 4\sqrt{43}).
