EF is the median of trapezoid ABCD.

Answer:Part A) [tex]x = 11[/tex]B) length of BC =  x + 12 =  x + 12 = 11 + 12 =23length of EF =  4x - 18 =  4(11) - 18 = 44 - 18 =26length of AD =  3x - 18 =  3(11) - 4 = 33 - 4 =29Step-by-step explanation:Median of trapezium is [tex]m=\frac{base1+base2}{2}[/tex]In provided figure, base1 is x+12 and base2 is 3x-4A) solve for value of xcalculate the median [tex]m=\frac{base1+base2}{2}[/tex][tex]4x-18=\frac{x+12+3x-4}{2}[/tex][tex]4x-18=\frac{4x+8}{2}[/tex][tex]4x-18=2x+4[/tex][tex]2x-18=4[/tex][tex]2x = 18 + 4[/tex][tex]2x = 22[/tex][tex]x = 11[/tex]B) To find the length of BC, AD and EF , put the value of x in equation of lineslength of BC =  x + 12 =  x + 12 = 11 + 12 =23length of EF =  4x - 18 =  4(11) - 18 = 44 - 18 =26length of AD =  3x - 4 =  3(11) - 4 = 33 - 4 =29