We can consider the side whose length is 28 feet as the base. However, we need to find the height. To do so, we will pay close attention to the right triangle formed by the height, a side, and a part of a nonparallel side.
We can see that the measure of two of the interior angles of the triangle are 30^(∘) and 90^(∘). We can use the Triangle Angle Sum Theorem to find the measure of the third angle.
180^(∘)- 90^(∘)- 30^(∘)=60^(∘)
The third angle measures 60^(∘) and, therefore, we have a 30^(∘)-60^(∘)-90^(∘) triangle. In this type of triangle the length of the longer leg is sqrt(3)2 times the length of the hypotenuse. With this information, and knowing that the hypotenuse measures 30 feet, we can find the length of the longer leg.
Longer Leg: sqrt(3)/2 * 30=15sqrt(3)
Therefore, the height of the parallelogram is 15sqrt(3)ft.
Now that we know that the base is 28 feet and that the height is 15sqrt(3) feet, we can substitute these values in the formula for the area of a parallelogram.
