The lateral side of the trapezoid is 4, and one of the corners adjacent to it is 30 °. Find the area of the trapezoid if its bases are 2 and 5

The area of the trapezoid is calculated by the formula S = (a + b) / 2 * h, where a and b are the bases of the trapezoid, and h is the height of the trapezoid. Denote the angles of the trapezoid A, B, C and D. And draw a height from the angle B to the base AD, as shown in the figure.
The resulting triangle ABP is rectangular with BP and AP legs. Note that BP is a leg that lies at an angle of 30 °, therefore it is equal to half the hypotenuse (by the property of a right triangle), h = 4/2 = 2. Using the trapezoid area formula, we get S = (2 + 5) * 2/2. Calculate S = 7.
Answer: S = 7.

Remember: The process of learning a person lasts a lifetime. The value of the same knowledge for different people may be different, it is determined by their individual characteristics and needs. Therefore, knowledge is always needed at any age and position.