The bases of the trapezoid are 9 and 54, one of the sides is 27, and the cosine of the angle between

The bases of the trapezoid are 9 and 54, one of the sides is 27, and the cosine of the angle between it and one of the bases is √65 ninths. Find the area of the trapezoid.

Let’s take the base of the trapezoid a = 54, b = 9, side c = 27. The cosine of the angle A: cos A = (√65) / 9.

Trapezoid height h = c * sin A = c * √ (1 – sin ^ 2 (A)] = 27 * √ [1 – 65 / (9) ^ 2] = 27 * 4/9 = 12.
Trapezium area = [(a + b) / 2] * h = [(54 + 9)] / 2 * 12 = 63 * 6 = 378.