Question

On a coordinate plane, parallelogram A B C D has points (3, 6), (6, 5), (5, 1), and (2, 2). What is the area of parallelogram ABCD? 13 square units 14 square units 15 square units 16 square units Mark this and return

Answer 1

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

Area = base x height

We can find the base by taking the distance between points A and B, or between points C and D. We can find the height by taking the distance between points B and C, or between points A and D.

Using the distance formula, we can find that the distance between points A and B is sqrt(10), and the distance between points B and C is sqrt(26).

Since both pairs of opposite sides of a parallelogram are parallel and congruent, we can use either pair of distances as the base and either pair of distances as the height.

Therefore, the area of parallelogram ABCD is:

Area = base x height
Area = sqrt(10) x sqrt(26)
Area = sqrt(260)
Area = 2sqrt(65)

So the area of parallelogram ABCD is approximately 16 square units.