What is the area of the trapezoid given top is 14, one side is 7, and bottom corner is 65°?

To find the area of a trapezoid, you need to know the lengths of the two parallel sides (the top and bottom) and the distance between them (the height or altitude). In this case, you are given the length of the top side as 14, one of the side lengths as 7, and the measure of one of the bottom angles as 65°.

To find the area of the trapezoid, you need to follow these steps:

Step 1: Identify the two parallel sides.
In this case, the top side is given as 14.

Step 2: Find the length of the other parallel side.
To find the length of the bottom side, we need to use the given information about the angle and the side length.

Step 3: Calculate the length of the bottom side.
Since we know one side is 7 and the adjacent angle is 65°, we can use trigonometry to find the length of the bottom side. By using the Cosine function, we can determine that the length of the bottom side is given by the formula:
Bottom side = adjacent side / cosine(angle)
Bottom side = 7 / cos(65°)

Step 4: Calculate the area of the trapezoid.
The area of a trapezoid is given by the formula:
Area = (base1 + base2) * height / 2

In this case, the base1 is the length of the top side (14), base2 is the length of the bottom side (obtained in step 3), and the height is not given. The height is the perpendicular distance between the two parallel sides.

Without the height, it is not possible to calculate the area of the trapezoid accurately. If you have the height, you can substitute the values into the formula to find the area.