In the trapezoid ABCD AD is a larger base. A straight line is drawn through the vertex B, parallel to CD

| June 25, 2021 | education

In the trapezoid ABCD AD is a larger base. A straight line is drawn through the vertex B, parallel to CD at point E, BC = 7 cm., AE-4, see find: a) the length of the middle line of the trapezoid; b) the perimeter of the trapezoid, if the perimeter of the ABE triangle is 17 cm

The quadrangle BCDE is a parallelogram, since BC is parallel to DE, as the base of a trapezoid, CD is parallel to BE by condition. Then BE = CD, BC = DE = 7 cm.

Determine the length of the larger base AD = AE + DE = 4 + 7 = 11 cm.

By condition, the perimeter of the ABE triangle is 17 cm.

Rave = AB + BE + AE = 17 cm.

(AB + BE) = 17 – AE = 17 – 4 = 13 cm.

Since BE = CD, then (AB + BE) = (AB + CD) = 13 cm.

Then the perimeter of the trapezoid is: Ravsd = (AB + CD) + BC + AD = 13 + 7 + 11 = 31 cm.

Determine the length of the midline of the trapezoid.

KM = (BC + AD) / 2 = (7 + 11) / 2 = 9 cm.

Answer: The perimeter of the trapezoid is 31 cm, the middle line is 9 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.