This is what I came up with when I solved for the intersection of those two lines.
Substituting  into , we get
Substituting this into , we get
So, D(10, -2) is the intersection.
Using A(2, 2), C(0, 8), D(10, -2), you can find the area.
Here are a couple of ways you might want to consider to find the area of triangle ACD.
(1) Using determinants
Remember to take the absolute value of this determinant to ensure a positive area.
(2) Heron's formula
where and a, b, c are the lengths of the sides of the triangle.
Here, you'll have to find the lengths of each side using the distance formula. Then use Heron's formula to determine the area: