In the trapezoid, one of the corners is 120o, and its bases are 10cm and 18cm. Find the area and perimeter of the trapezoid.

univerkov | September 15, 2021 | education

In an isosceles trapezoid, the height drawn from the apex of an obtuse angle cuts off two segments on the larger base, the smaller of which is equal to the half-difference of the trapezoid bases. DН = (АD – ВС) / 2 = 8/2 = 4 cm.

In a right-angled triangle СDН, the angle DСН = 180 – 90 – 60 = 30. Then the leg DН lies opposite the angle 30, and therefore is equal to half the length of the hypotenuse CD. DH = CD / 2.

CD = AB = 2 * DH = 2 * 4 = 8 cm.

Let’s define the perimeter of the trapezoid. P = AB + BC + CD + AD = 8 + 10 + 8 + 18 = 44 cm.

Determine the area of the trapezoid. Savsd = (ВС + АD) * СН / 2 = (10 + 18) * 4/2 = 28 * 4/2 = 56 cm2.

Answer: The perimeter of the trapezoid is 44 cm, the area of the trapezoid is 56 cm2.

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.