Question

Find the area of the parallelogram whose vertices are listed. (−3,−2),(0,4),(3,−4),(6,2) The area of the parallelogram is square units.

Answer 1

To find the area of a parallelogram, use the formula Area = base x height. Choose one side as the base, calculate its length, and find the perpendicular distance between the base and its opposite side to determine the height. Use these values to calculate the area.

Step-by-step explanation:

To find the area of a parallelogram, we can use the formula:

Area = base x height

In this case, we can choose any side of the parallelogram as the base and the perpendicular distance between the base and its opposite side as the height.

Let's choose the side connecting the points (-3,-2) and (0,4) as the base. The length of this side is 5 units (using the distance formula).

The perpendicular distance between this side and its opposite side can be found by calculating the distance between the point (3,-4) and the line passing through the base. Using the formula for the distance between a point and a line, we find that the distance is 5 units.

Therefore, the area of the parallelogram is 5 x 5 = 25 square units.

Answer 2

To find the area of a parallelogram, use the base times height formula. Calculate the length of the base and height using the coordinates of the vertices which is 32 square units

Step-by-step explanation:

To find the area of a parallelogram, we can use the formula:

Area = base * height

In this case, we can use the coordinates of the vertices to find the length of the base and height.

Let's label the vertices as A(-3,-2), B(0,4), C(3,-4), and D(6,2).

The base of the parallelogram is the distance between points A and B, which is 4 units.

The height of the parallelogram is the perpendicular distance between the base and point C (or D). We can find this distance by calculating the difference in the y-coordinates of C (or D) and B, which is 8 units.

So, using the formula, the area of the parallelogram is:

Area = 4 * 8 = 32 square units