The diagonals of a trapezoid are perpendicular and have lengths 8 and 10. find the length of the median of the trapezoid.

We have to use Pythagorean theorem ( see the picture in the attachment ):
( a + b )² = 10² + 8²  ( where a and b are the bases of a trapezoid )
( a + b )² = 100 + 64
( a + b )² = 164
a + b = √164
a + b = 12.8 
We don`t need to find a and b, because we have a formula for the length of the median which is:
m = ( a + b ) / 2 
m = 12.8 / 2

m = 6.4