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Since the height, the base, and one of its congruent sides make a triangle, therefore we can use Pythagorean theorem.

Subtract both sides by 36

Now since the parallel sides of a trapezoid are congruent, we can say that 2 of the sides have the same length

Next I came up with my own formula that:
or simply

where z is the length we got from the Pythagorean theorem

The formula of the area of the trapezoid is:
A=246 m²
h=6 m
Substitute the values

246 m²=\frac{1}{2}6 m(b_{1}+b_{1}+16 m)
Multiply both sides by 2
492 m²=6 m(2b_{1}+16)
Divide both sides by 6
82 m=2b_{1}+16
Subtract both sides by 16
66 m=2b_{1}
Divide both sides by 2
33 m=b_{1}

Now we know we have base 1 with 33 m, not lets substitute to find the longer base
b_{2}=33 m+16 m
Add like terms
b_{2}=49 m

Hope this helps =)