The given information states that AC is parallel to BD, and we need to find the area and perimeter of triangles DOC and ABC. Let's calculate them step by step.

First, let's find the length of AD and BC. Since AC is parallel to BD, we can use the property of similar triangles. Triangle AOD is similar to triangle BOC.

Using the property of similar triangles, we can set up the following ratio:

AD / OD = BC / OC

Substituting the given values, we have:

AD / 12 = BC / 42

Simplifying the equation, we find:

AD = (12 * BC) / 42

AD = (2 * BC) / 7

Now, let's find the length of BD. Since AC is parallel to BD, triangle ABD is similar to triangle BDC. Using the property of similar triangles, we can set up the following ratio:

AD / AC = BD / BC

Substituting the given values, we have:

(2 * BC) / 7 = BD / 28

Simplifying the equation, we find:

BD = (4 * BC) / 7

Now that we have the lengths of AD and BD, we can find the length of AB:

AB = AD + BD

AB = (2 * BC) / 7 + (4 * BC) / 7

AB = (6 * BC) / 7

Next, let's find the area of triangle DOC. We can use the formula for the area of a triangle:

Area = (base * height) / 2

In triangle DOC, the base is OD and the height is BC. Substituting the given values, we find:

Area(DOC) = (12 * BC) / 2

Area(DOC) = 6 * BC

Finally, let's find the perimeter of triangle ABC. The perimeter is the sum of the lengths of all three sides:

Perimeter(ABC) = AB + AC + BC

Substituting the previously found values, we have:

Perimeter(ABC) = (6 * BC) / 7 + 28 + BC

Perimeter(ABC) = (13 * BC) / 7 + 28

In conclusion:
- The area of triangle DOC is 6 times the length of BC.
- The perimeter of triangle ABC is (13 times the length of BC divided by 7) plus 28.