In an isosceles trapezoid, one of the angles is 60 degrees, the sides are 8 cm

| September 8, 2021 | education

In an isosceles trapezoid, one of the angles is 60 degrees, the sides are 8 cm and the smaller base is 7 cm. Find the middle line of the trapezoid.

Let’s draw two heights BH and СK from the vertices of the obtuse angles of the trapezoid. In a right-angled triangle ABH, the angle ABH = 180 – 90 – 60 = 30, then the leg AH is located opposite the angle 30, which means that its length is equal to half the length of the hypotenuse AB. AH = AB / 2 = 8/2 = 4 cm.

Since the trapezoid is isosceles, the triangles ABH and CDK are equal in the third sign of equality of right-angled triangles, hypotenuse and acute angle, then DK = AH = 4 cm.

Since BCКН is a rectangle, then НK = BC = 7 cm, then AD = AH + НK + KD = 4 + 7 + 4 = 15 cm.

Determine the length of the midline of the trapezoid.

KM = (BC + AD) / 2 = (7 + 15) / 2 = 22/2 = 11 cm.

Answer: The middle line of the trapezoid is 11 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.