Answer:
AC = 12
Explanation:
You want the length of diagonal AC in trapezoid ABCD with AD=BD=CD=6.5 and BC=5.
Semicircle
A semicircle of radius 6.5 centered at D will pass through points A, B, C and will intersect line CD at E. Then CE=13, and AE=5 by symmetry to BC.
Triangle EAC is a right triangle with leg EA=5 and hypotenuse EC=2·6.5=13. Then diagonal AC can be found from the Pythagorean theorem:
EC² = AE² +AC²
13² -5² = AC² = 169 -25 = 144
AC = √144 = 12
The length of diagonal AC is 12.