To the nearest tenth, what is the area in square inches of a parallelogram with two acute angles of 37°, a side length of 18 inches, and a base of 28 inches?

To determine the area of the parallelogram, we use the formula for the area given the base and the height. The area is calculated as follows:

Area = base × height.

In this case, the base is given as 28 inches. To find the height, we need to relate it to the side length and the angle. The height can be calculated using the sine function, which is relevant in trigonometry when dealing with the heights of triangles and parallelograms.

Given that one of the acute angles is 37° and the side length (which can act as the side corresponding to the height) is 18 inches, we can find the height using the angle:

Height = side length × sin(angle)

Height = 18 inches × sin(37°).

Using a calculator, we find that sin(37°) is approximately 0.6018. Thus, the height becomes:

Height ≈ 18 inches × 0.6018 ≈ 10.83 inches.

Now, we can substitute the base and the height back into the area formula:

Area = 28 inches × 10.83 inches ≈ 303.3 square inches.

Thus, rounding to the nearest tenth, the