# 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

May 31, 2020 | Education

| 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.

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