The area of the given figure ABCD with respective coordinates is
24 square units.
What is the area of quadrilateral?
The area of a quadrilateral is nothing but the region enclosed by the sides of the quadrilateral.
Given the coordinates of the quadrilateral as; A(−4, 1), B(2, 1), C(2, −5), and D(−4, −3).
By inspection, we see that the y coordinates of A and B are the same. Thus, their length will be the difference of their x coordinates. Thus;
AB = 2 - (-4)
AB = 6
Similarly, B and C have same x coordinates. Thus;
BC = -5 - 1 = -6
A and D have same x coordinate and as such;
AD = -3 - 1 = -4
AB and BC are perpendicular to each other because of opposite signs of same Number and since AD has a different length, then we can say that the figure ABCD is a rectangle.
Thus;
Area of figure = 6 × 4 = 24 square units.
The area of the given figure ABCD with respective coordinates is
24 square units.
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