Areas of Parallelograms and Triangles question bank (Maths)

In the figure,$ABCD$ is a parallelogram and $EFCD$ is a rectangle. Also,$AL \perp DC$. Prove that:
$(i)$ $\text{ar}(ABCD) = \text{ar}(EFCD)$
$(ii)$ $\text{ar}(ABCD) = DC \times AL$

If a triangle and a parallelogram are on the same base and between the same parallels,then prove that the area of the triangle is equal to half the area of the parallelogram.