find the area

We have a rhombus

1/2  the length of  the other diagonal is    sqrt (10^2  - 5^2)   =sqrt  (100  - 25)  =sqrt (75)  = 5sqrt (3)

The diagonal lengths =  10 , 10sqrt (3)

Area   = product of  the diagonals  /  2  =    (10 * 10 sqrt (3) )   / 2  =  50 sqrt (3)