Answer:

Step-by-step explanation:
Since there are 2 diagonal angles that are 90 degrees, we can figure out the shape is made of 2 right triangles, so we can use the Pythagorean theorem to find out the length of each side.
The problem said that there must be 2 distinct sides with integer lengths, but there are no 2 integers that satisfy
so we can deduce that both right triangles contain 1 integer value side and 1 non-integer value side.
There are only 2 positive integer values that would fit in
for x: 1 and 2. That means the 2 triangles' equation is:
and
.
Now, since these are right triangles, their areas are just going to be their 2 legs multiplied by 1/2.
The first triangle's area is:

The second triangle's area is:

The total area of the quadrilateral would be the sum of the 2 triangles, which is just
.
I hope this helped you.