The larger base of an isosceles trapezoid is 12 cm, its lateral side is 4 cm and the angle between them is 60 degrees.

| March 15, 2021 | education

The larger base of an isosceles trapezoid is 12 cm, its lateral side is 4 cm and the angle between them is 60 degrees. Find the length of the smaller base.

Let’s build the height of the HВ trapezoid ABCD.

Triangle ABH is rectangular, in which the angle ВAН, by condition, is equal to 60, then the angle AВН = 90 – 60 = 30.

Leg AH lies opposite angle 30, then its length is equal to half the length of the hypotenuse AB.

AH = AB / 2 = 4/2 = 2 cm.

Let’s build the CM height. Since the trapezoid is isosceles, then AB = CD, angle BAН = CDM, then right-angled triangles ABH and CDM are equal in hypotenuse and acute angle. Then DМ = АН = 2 cm.

The length of the segment MH = AD – AH – DM = 12 – 2 – 2 = 8 cm.

Quadrangle BCMN is a rectangle, then BC = MH = 8 cm.

Answer: The length of the smaller base is 8 cm.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.