Since the height, the base, and one of its congruent sides make a triangle, therefore we can use Pythagorean theorem.
10²=a²+6²
100=a²+36
Subtract both sides by 36
64=a²
a=8
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:
[tex]b_{2}=b_{1}[/tex]+2z
or simply
[tex]b_{2}=b_1[/tex]+16
where z is the length we got from the Pythagorean theorem
The formula of the area of the trapezoid is:
A=[tex]\frac{1}{2}h(b_{1}+b_{2}[/tex]
A=246 m²
h=6 m
Substitute the values
246 m²=[tex]\frac{1}{2}6 m(b_{1}+b_{1}[/tex]+16 m)
Multiply both sides by 2
492 m²=6 m([tex]2b_{1}[/tex]+16)
Divide both sides by 6
82 m=[tex]2b_{1}[/tex]+16
Subtract both sides by 16
66 m=[tex]2b_{1}[/tex]
Divide both sides by 2
33 m=[tex]b_{1}[/tex]
Now we know we have base 1 with 33 m, not lets substitute to find the longer base
[tex]b_{2}[/tex]=33 m+16 m
Add like terms
[tex]b_{2}[/tex]=49 m
Hope this helps =)
