Question

why the formula for the area of a trapezoid this A=1/2 x h x(a+b)

Answer 1

draw any trapezoid
draw a diagonal

isn't the height between the two parallel sides constant? Let it be h
let the two parallel sides be a and b

so now you have two triangles where you know the height, h, and the sides
first triangle area = (1/2)ah
2nd triangle area = (1/2)bh

total = (1/2)ah + (1/2)hb
common factor of (1/2)h
gives us
(1/2)h(a+b)