in fig. angle BAD= angle ADC = 90 and AX parallel BC ; the area of abcx

To find the area of ABCX, we need more information about the figure. Specifically, we need to know the lengths of the sides or any other relevant measurements. Without this information, it is not possible to determine the exact area of the figure.

However, I can provide you with a general explanation on how to find the area of a quadrilateral. The area of a quadrilateral can be calculated using various methods depending on the information available.

One common method is to divide the quadrilateral into smaller triangles and then calculate the area of each triangle separately using the formula for the area of a triangle:
Area = (1/2) * base * height

In this case, you can divide the quadrilateral ABCX into two triangles, either by drawing a diagonal from A to C or from B to D. Then, calculate the area of each triangle using the formula mentioned above. Finally, add the areas of both triangles to get the total area of ABCX.

Keep in mind that without additional information, this explanation remains general and cannot provide an exact answer for the area of ABCX.