The large side of the rectangular trapezoid is 2, and one of the corners at the lower base is 30 degrees.

The large side of the rectangular trapezoid is 2, and one of the corners at the lower base is 30 degrees. the smaller base is 5. Find the area of the trapezoid.

Let ABCD be a given trapezoid (∠A = 90 °).

Let us lower the height from the top of C to the bottom of AD.

The CED triangle is rectangular.

Because a leg lying opposite an angle of 30 ° is equal to half of the hypotenuse, then CE = ½ CD = ½ * 2 = 1.

By the Pythagorean theorem, we find ED.

ED ^ 2 = CD ^ 2 – CE ^ 2 = 4 – 1 = 3.

ED = √3.

AD = AE + ED = BC + ED = 5 + √3.

S = 1/2 (BC + AD) * CE = ½ (5 + 5 + √3) * 1 = ½ (10 + √3) = 5 + √3 / 2.

Answer: the area of the trapezoid is 5 + √3 / 2.