Find the area of the quadrilateral whose vertices taken in order are A (1,1), B C (7, −3), (12,2) , D(7,21). ?

To find the area of a quadrilateral, we can divide it into two triangles and find the sum of their areas.

First, let's find the area of triangle ABC. We can use the formula for the area of a triangle given its vertices:

Area of triangle ABC = 1/2 * |(x1(y2-y3) + x2(y3-y1) + x3(y1-y2))|

Plugging in the coordinates of A, B, and C, we get:

Area of triangle ABC = 1/2 * |(1(-3-2) + 7(2-1) + 7(1-(-3)))|
= 1/2 * |(-5 + 7 + 28)|
= 1/2 * |30|
= 15

Next, let's find the area of triangle ACD. Again, we can use the formula for the area of a triangle given its vertices:

Area of triangle ACD = 1/2 * |(x1(y2-y3) + x2(y3-y1) + x3(y1-y2))|

Plugging in the coordinates of A, C, and D, we get:

Area of triangle ACD = 1/2 * |(1(2-21) + 7(21-1) + 12(1-2))|
= 1/2 * |(-19 + 140 + -12)|
= 1/2 * |109|
= 54.5

Finally, we can find the area of the quadrilateral by summing the areas of the two triangles:

Area of quadrilateral ABCD = Area of triangle ABC + Area of triangle ACD
= 15 + 54.5
= 69.5

Therefore, the area of the quadrilateral ABCD is 69.5 square units.