Find the area of the quadrilateral `A B C D` having vertices `A(1,1),B(7,-3),C(12 ,2),` and `D(7, 21)dot`

Explanation

To find the area of quadrilateral ABCD with vertices A(1,1), B(7,-3), C(12,2), and D(7,21), we can divide the quadrilateral into two triangles: ABD and BCD. We will calculate the area of each triangle separately and then sum them to get the total area of the quadrilateral.

### Step 1: Calculate the area of triangle ABD

The coordinates of the vertices of triangle ABD are:
- A(1, 1) → (x1, y1)
- B(7, -3) → (x2, y2)
- D(7, 21) → (x3, y3)
...