What is the area of a parallelogram whose vertices are A(−12, 2) , B(6, 2) , C(−2, −3) , and D(−20, −3)

Final answer:

The area of the parallelogram with the given vertices is calculated using the base and height found from the coordinates, which yields an area of 90 square units.

Explanation:

The student wants to know the area of a parallelogram with given vertices A(-12, 2), B(6, 2), C(-2, -3), and D(-20, -3). To find this area, we can use the distance formula to calculate the lengths of adjacent sides and then find the product of one side's length and the absolute value of the other side's perpendicular height to it. First, we determine the lengths of sides AB and AD which are parallel to the x and y axes, respectively, thereby simplifying our calculations.

Side AB is horizontal, so we can find its length by the difference in x-coordinates: Length of AB = |xB - xA| = |6 - (-12)| = 18 units. Side AD is vertical, so its length is determined by the difference in y-coordinates: Length of AD = |yD - yA| = |(-3) - 2| = 5 units.

The area of the parallelogram is then the product of the base, AB, and the height, AD, which is equal to 18 units * 5 units = 90 square units.

The area of the parallelogram with given vertices is 90 square units, calculated by multiplying the base length AB (18 units) by the height AD (5 units).

To find the area of a parallelogram with vertices A(−12,  2), B(6,  2), C(−2,  −3), and D(−20,  −3), we can calculate the base and the height of the parallelogram. Since points A and B lie on the same horizontal line (they have the same y-coordinate), AB can be considered as the base. To calculate the length of AB, we simply subtract the x-coordinate of A from that of B:

Base AB = xB - xA = 6 - (−12) = 18 units

Points B and C form one of the sides BC of the parallelogram, but because they do not form a vertical line, we cannot directly take BC as the height. Instead, point D has the same x-coordinate as point A which means line AD is vertical, and thus the height can be found by subtracting the y-coordinate of D from that of A:

Height AD = yA - yD = 2 - (−3) = 5 units

The area of a parallelogram is calculated as the product of its base and height:

Area = Base × Height = 18 units × 5 units = 90 square units

Therefore, the area of the parallelogram is 90 square units.

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