Draw a trapezium say abcd and join the diagonals you will obtain two triangle draw two perpendiculars on diagonals from both parallel sides 
now area of quadrilateral(trapezium)=sum of area of both the triangles
        let a and b be two parallel sides and h be the perpendiculars 
area of 1st triangle=1/2 x a  x h  ....1
 area of 2nd triangle=1/2 x b x h .........2
                      sum of 1 and 2 = area of quadrilateral(trapezium)
1/2 x a x h +1/2 x b x h= area of trapezium       
1/2 x (a+b) x h= area of trapezium             (taking out 1/2 as common)

thus proved............

The formula of trapezium is 1/2*dh