Question

write the area of the trapezoid in terms of a and b

Answer 1

i think it's the first one...

the area of the trapezoid is the area of the two purple triangles plus the area of the yellow triangle:
a*b + (1/2)*c^2

but since the c^2=a^2+b^2 you can substitute that into the formula:
a*b + (1/2)(a^2 + b^2)

Answer 2

in your first choice, (1/2)(a+b)^2 = (1/2)(a^2 + 2ab + b^2) =
can you take it from here?