In parallelogram ABCD, BC = 8, DC = 12, and measure of angle D is 50 degrees. Find the area of the parallelogram to the nearest tenth.

The height is 8*sin50 = 6.13

a = 12*6.13

To find the area of a parallelogram, we need to know the length of one side and the height (or altitude) of the parallelogram.

In this case, we have the length of one side, BC, which is 8 units. However, we do not have the height or altitude given directly.

To find the height of the parallelogram, we can use trigonometry. By drawing a perpendicular line from D to the line segment BC, we can form a right triangle.

Let's call the point where the perpendicular line meets BC, point E. Now, we have right triangle EDC, where angle DEC is 90 degrees.

In triangle EDC, we have the length of the base DC, which is 12 units, and the measure of angle D, which is 50 degrees.

To find the height, we need to find the length of line segment DE. We can use the trigonometric function tangent (tan) because we have the opposite (DE) and adjacent (DC) sides.

tan(D) = DE / DC
tan(50°) = DE / 12

Now, we can solve for DE:
DE = tan(50°) * 12

Using a calculator, we can find that DE is approximately 14.49 units.

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

Area = base * height

In this case, the base is BC, which is 8 units, and the height is DE, which is approximately 14.49 units.

Area = 8 * 14.49
Area ≈ 115.92

Therefore, the area of the parallelogram ABCD is approximately 115.9 square units to the nearest tenth.