To the nearest tenth, what is the area of a parallelogram with two acute angles at 24.2 degrees, side length of 11 cm, and base of 23.2 cm?

To find the area of a parallelogram, the formula used is:

[

\text{Area} = \text{base} \times \text{height}

]

In this problem, the base of the parallelogram is given as 23.2 cm. However, we also need to determine the height, which is crucial in calculating the area.

The height can be found using the relationship between the angle, the side length, and the height. The height (h) corresponding to the angle (θ) can be found using the sine function:

[

h = \text{side length} \times \sin(\theta)

]

Given that one of the acute angles is 24.2 degrees and the side length is 11 cm, we can calculate the height as follows:

[

h = 11 , \text{cm} \times \sin(24.2^\circ)

]

Using a calculator, we find:

[

\sin(24.2^\circ) \approx 0.409

]

Thus,

[

h \approx 11 , \text{cm} \times 0.409 \approx 4.5 , \text