Find the area of a parallelogram with sides of length 6 and 8, and with an interior angle with measure $45^\circ$.
6 * 8 * sin45°
To find the area of a parallelogram, we can use the formula:
Area = base × height
In this case, the base of the parallelogram is 6 units. To find the height, we need to use the given information about the interior angle.
The height of the parallelogram is the perpendicular distance between the base and the opposite side. Since the interior angle is $45^\circ$, we can use trigonometry to find the height.
In a right triangle with one angle measuring $45^\circ$, the legs are equal. Thus, the height of the parallelogram is also 6 units.
Now we can calculate the area:
Area = base × height
= 6 units × 6 units
= 36 square units
Therefore, the area of the parallelogram is 36 square units.