A(6,1) , B (8,2) and C (9,4) are three vertices of a parallelogram ABCD . If E is the mid - point of DC , then find the area of `triangle`ADE.

Explanation

To find the area of triangle ADE given the vertices A(6, 1), B(8, 2), and C(9, 4) of a parallelogram ABCD, and knowing that E is the midpoint of side DC, we can follow these steps:

### Step 1: Find the coordinates of point D
Since the diagonals of a parallelogram bisect each other, we can find the coordinates of point D by using the midpoint formula.

Let the coordinates of D be (X, Y). The midpoint P of diagonal AC is given by:
\[
P = \left( \frac{x_A + x_C}{2}, \frac{y_A + y_C}{2} \right) = \left( \frac{6 + 9}{2}, \frac{1 + 4}{2} \right) = \left( \frac{15}{2}, \frac{5}{2} \right)
...