The lengths of the parallel sides of a trapezium are 51 cm and 21 cm, and that of each ofthe other two sides is 39 cm. What is the area (in cm$$^2$$) of the trapezium?

We draw the trapezium is given below 

From the above diagram, we apply the Pythagoras theorem   in $$ \triangle ABC $$

  then $$( AC)^2 = (39)^2 - (15)^2 $$

$$\Rightarrow (AC)^2 = 1521 - 225 $$

$$\Rightarrow (AC)^2 = 1296 $$

$$\Rightarrow AC = 36 $$

then Area of trapezium = $$ \frac {1}{2} \times  (sum of sides) \times  (Distance between them) $$

                                = $$ \frac {1}{2} \times (21+51) \times (36) $$

                                    = $$ \frac {1}{2} \times 72 \times 36 $$

                                   =  $$36 \times 36 $$

                                  = $$ 1296 cm^2 $$ Ans