Identify the given values

Given the area $A = 80$, parallel sides $a = 13.5$, and $b = 6.5$. We need to find the height $h$.

$A = 80, a = 13.5, b = 6.5$

Apply the Trapezium Area Formula

Substitute the known values into the standard area formula for a trapezium.

$80 = \frac{1}{2} \times (13.5 + 6.5) \times h$

Simplify and Calculate

Sum the parallel sides: $13.5 + 6.5 = 20$. Then, solve for $h$: $80 = 10 \times h$, so $h = 8$.

$80 = \frac{1}{2} \times 20 \times h \Rightarrow h = \frac{80}{10} = 8$