In-depth answers would be greatly appreciated!

Trapezoid means different things in different countries.

I am assuming that you mean a 4 sided figure where 2 of the sides are parallel. (I would call this a trapezium)

I am wondering if you are referring to what I would call an isoscles trapezium where the 2 non parallel sides are equal in length?

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

HI Melody;

Yes, it is a rhombus. It is not different. A rhombus is a special parallelogram and a parallelogram is a special trapezoid.

The diagonals should be perpendicular to each other.

Sorry for the confusion, I am working with the definition that a trapezoid is a quadrilateral in which exactly one pair of opposite sides are parallel.

Also answered here!

https://web2.0calc.com/questions/sorry-to-re-post-this-but-i-m-afraid-it-will-get

I was not convinced there was an answer to this question so I decided to experiment with Geogebra to get an answer.

Bummer!!

 I only just saw the word perpendicular. What a goose I am.    

I guess the pic I drew is not relevant after all!!