The quadrilateral ABCD is specified on the coordinate plane. Find its area if A (-1; -2), B (-3; 2), C (5; 6), D (5; 1).

If we find the specified points on the coordinate plane and connect them into a quadrangle ABCD, we can see that we are given a rectangular trapezoid, where AD and BC are the bases of the trapezoid, AB and CD are its lateral sides, AB is perpendicular to AD and BC and is the height of this trapezoid.

The area of ​​such a trapezoid is calculated by the formula

S = (AD + BC): 2 * AB

Let’s find the lengths of the sides by their coordinates:

d = √ ((x2-x1) ² + (y2-y1) ²), where d is the calculated segment, x1, x2 are the abscissas of the beginning and end of the segment, y1, y2 are the ordinates of the beginning and end of the segment. Substitute the values ​​and find:

AD = √45 = 3√5

BC = √80 = 4√5

AB = √20 = 2√5

Now we substitute the obtained values ​​into the formula for the area of ​​a rectangular trapezoid and make the calculations:

S = (3√5 + 4√5): 2 * 2√5 = 7√5 * √5 = 7 * 5 = 35

Answer: the area of ​​a given quadrilateral AVSD is 35 units squared.