The diagonals of an isosceles trapezoid are mutually perpendicular, find the area of the trapezoid if its midline is 6.

From the properties of an isosceles trapezoid, it is known that if its diagonals are perpendicular, then its height will be equal to the half-sum of the bases. The midline of the trapezoid is also equal to the half-sum of the bases. Thus, we can conclude that in this case, the middle line of the trapezoid is equal to the height of the trapezoid.
The area of the trapezoid can be found by the formula:
S = m * h,
where m is the middle line, h is the height.
S = 6 * 6 = 36
Answer: the area of the trapezoid is 36.