The bases of an isosceles trapezoid are equal to A and B, the lateral side is C. Find the diagonal of the trapezoid.

To determine the diagonal of the trapezoid, we need to find the height of the HV.

Since the trapezoid is isosceles, then AH = (AD – BC) / 2 = (in – a) / 2.

DH = (AD + BC) / 2 = (b + a) / 2.

Then, from the right-angled triangle ABH, by the Pythagorean theorem, BH ^ 2 = AC ^ 2 – AH ^ 2 = c2 – ((s – a) / 2) ^ 2.

Let’s define the diagonal BD from the triangle HBD.

BD ^ 2 = BH ^ 2 + DH ^ 2 = c ^ 2 – ((b – a) / 2) ^ 2 + ((b + a) / 2) ^ 2 = c2 – ((b – a) 2 + (b + a) ^ 2) / 4 = c ^ 2 + (a ^ 2 + b ^ 2) / 2.

VD = √ (c ^ 2 + (a ^ 2 + b ^ 2) / 2).

Answer: The length of the diagonal is √ (c2 + (a2 + b2) / 2).