Question

Which statement is correct regarding the measurements of the parallelogram?

Answer 1

Answer:

The base is 8 and the height is 3, so the area is 8 (3) = 24 square units.

Step-by-step explanation:

The area of the parallelogram is given by the following expression:

$A = \|\vec u\times \vec v\|$

The vectors are, respectively:

$\vec u = (10-2, 1 - 1,0-0)$

$\vec u = (8,0,0)$

The base of the parallelogram is 8 units.

$\vec v = (8-2, 4-1,0-0)$

$\vec v = (6,3,0)$

The height of the parallelogram is 3 units.

The cross product of both vectors is:

$\vec u \times \vec v = (0,0,24)$

The area of the parallelogram is given by the norm of the resulting vector:

$\|\vec u \times \vec v\| = 24$

Answer 2

Answer:

B. The base is 8 and the height is 3, so the area is 8 (3) = 24 square units.