Find the area of the parallelogram ABCD if the area of the triangle ABC is 36cm ^ 2.

So, to get a parallelogram, we complete ▲ ABC.
Given:
S (▲ ABC) = 36cm ^ 2
To find:
S (ABCD)
Decision:
Consider ▲ ABC and ▲ BCD. In them:
1) BC – common side;
2) ∠BAC = ∠BDC (parallelogram property);
3) AC = BD (parallelogram property).
Conclusion: ▲ ABC = ▲ BCD.
Therefore, S (▲ ABC) = S (▲ BCD) = 36cm ^ 2.
Hence:
S (ABCD) = S (▲ ABC) + S (▲ BCD)
S (ABCD) = 36cm ^ 2 + 36cm ^ 2
S (ABCD) = 72cm ^ 2.
Answer: 72cm ^ 2.