**Finding the Length of the Sides**

To find the area of the quadrilateral ABCD, we first need to find the lengths of its sides. We can use the distance formula to calculate the lengths.

The distance formula is given by:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Using the distance formula, we can find the lengths of the sides AB, BC, CD, and DA.

- Length of AB:
d(AB) = sqrt((-4 - (-2))^2 + (-5 - 1)^2)
= sqrt((-4 + 2)^2 + (-5 - 1)^2)
= sqrt((-2)^2 + (-6)^2)
= sqrt(4 + 36)
= sqrt(40)
= 2√10

- Length of BC:
d(BC) = sqrt((-1 - (-4))^2 + (-6 - (-5))^2)
= sqrt((-1 + 4)^2 + (-6 + 5)^2)
= sqrt((3)^2 + (-1)^2)
= sqrt(9 + 1)
= sqrt(10)

- Length of CD:
d(CD) = sqrt((4 - (-1))^2 + (5 - (-6))^2)
= sqrt((4 + 1)^2 + (5 + 6)^2)
= sqrt((5)^2 + (11)^2)
= sqrt(25 + 121)
= sqrt(146)

- Length of DA:
d(DA) = sqrt((-2 - 4)^2 + (1 - 5)^2)
= sqrt((-2 - 4)^2 + (1 - 5)^2)
= sqrt((-6)^2 + (-4)^2)
= sqrt(36 + 16)
= sqrt(52)
= 2√13

**Calculating the Area**

To calculate the area of the quadrilateral ABCD, we can divide it into two triangles: ABC and CDA.

The area of a triangle can be calculated using the formula:
Area = 0.5 * base * height

In triangle ABC, the base is AB and the height can be found by dropping a perpendicular from C to AB.

The length of AB is 2√10, and the height can be calculated by finding the distance between C and the line AB.

Using the formula for the distance of a point from a line:
d = |Ax + By + C| / sqrt(A^2 + B^2)

The equation of line AB can be written as:
2x + 6y + 10 = 0

Substituting the coordinates of point C (-1, -6) into the equation, we get:
d = |2(-1) + 6(-6) + 10| / sqrt(2^2 + 6^2)
= |-2 - 36 + 10| / sqrt(4 + 36)
= |-28 + 10| / sqrt(40)
= |-18| / 2√10
= 18 / 2√10
= 9 / √10

Now, the height of triangle ABC is 9 / √10.

Plugging the values into the formula for