In trapezoid ABCD AB = BC = CD = 2√3. A = 60, find the length of the large base.

Let’s change the height of the ВН trapezoid ABCD.

In a right-angled triangle ABН, we determine the size of the DН leg.

Angle ABН = (180 – 90 – 60) = 30, then the length of the leg AH is equal to half the length of the hypotenuse AB.

AH = 2 * √3 / 2 = √3 cm.

Let’s draw the height of the CК. Triangles ABН and CDK are equal in hypotenuse and acute angle, since AB = CD, angle BAK = CDН. Then AH = DK = √3 cm.

The quadrilateral ВСНK is a rectangle, then НC = BC = 2 * √3 cm.

Determine the length of the larger base of the trapezoid.

AD = AH + НK + DK = √3 + 2 * √3 + √3 = 4 * √3 cm.

Answer: The length of the larger base is 4 * √3 cm.