The base of an isosceles trapezoid is 56 and 104, the side is 30. Find the length of the diagonal of the trapezoid.

The solution of the problem.
In an isosceles trapezoid, the height divides the larger base into parts equal to the half-sum and half-difference of the bases.
(104 + 56): 2 = 80;
(104-56): 2 = 24.
Find the height of the trapezoid by the Pythagorean theorem:
h = √ (30 ^ 2-24 ^ 2) = 18.
Knowing the height and most of the base (80), we find the diagonal by the Pythagorean theorem:
Diagonal = √ (80 ^ 2 + 18 ^ 2) = 82
Answer: The diagonal of the trapezoid is 82.