A straight line is drawn through vertex C of trapezoid ABCD, parallel to the lateral side AB. It crosses the large base AD

| January 9, 2021 | education

A straight line is drawn through vertex C of trapezoid ABCD, parallel to the lateral side AB. It crosses the large base AD at point K. The perimeter of the trapezoid ABCD is 37cm, DK = 6cm, AK = 9cm. Calculate: a) the length of the midline of the trapezoid; b) the perimeter of the triangle KCD.

Since SC is parallel to AB, ABCK is a parallelogram, and therefore BC = AK = 9 cm.
Then the middle line of the trapezoid will be equal to: MР = (AD + BC) / 2 = (9 + 6 + 9) / 2 = 12 cm.
By condition, the perimeter of the trapezoid is 37 cm.
AB + BC + CD + AD = 37.
AB + 9 + CD + 15 = 37.
AB + CD = 13 cm.
Since AB = CK, then CK + CD = 17.
The perimeter of the KCD triangle is equal to Pcsd = (CK + CD) + KD = 17 + 6 = 23 cm.
Answer: The middle line of the trapezoid is 12 cm, the perimeter of the KCD triangle is 23 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.