Find the area of a parallelogram with sides of length 6 and 8, and with an interior angle with measure 45 degrees.

The area of parallelogram is

Area=a*b*sin(θ)
where a, b are adjacent side lengths, and
θ is the included angle.

it is 24sqrt2

its 24sqrt2

To find the area of a parallelogram, we can use the formula: area = base x height.

In this case, the given lengths of the sides (6 and 8) are not the base and height of the parallelogram. However, we can use the given angle measurement of 45 degrees to find the height.

First, draw a diagram of the parallelogram. Label one of the sides with the length of 6 as the base, denoted as b. Let the interior angle with measure 45 degrees be θ. Then draw a perpendicular line from the opposite vertex to the base. This perpendicular line represents the height, denoted as h.

Now, we can use trigonometry to find the height of the parallelogram. In the right triangle formed by the height, base, and the perpendicular line, we have:

sin(θ) = opposite/hypotenuse

sin(45 degrees) = h/8

By substituting the value of sin(45 degrees) as 1/sqrt(2), we can solve for h:

1/sqrt(2) = h/8

Simplifying,

h = 8/sqrt(2) = 8 * sqrt(2)/2 = 4 * sqrt(2)

Now that we have found the height of the parallelogram, we can calculate the area using the formula:

Area = base x height

Area = 6 * 4 * sqrt(2) = 24 * sqrt(2)

Therefore, the area of the parallelogram is 24 * sqrt(2) square units.