# In trapezoid ABCD, AD-greater than the base through the vertex C, a straight line is drawn parallel to AB

**In trapezoid ABCD, AD-greater than the base through the vertex C, a straight line is drawn parallel to AB, until the intersection with AD point E DE = 6cm, AE = 11cm find 1) the length of the middle line of the trapezoid. Perimeter ABCD = 21cm**

1) By the condition of CE // AB, since ABCD is a trapezoid, then BC // AD, hence BC // AE, hence ABCE-parallelogram (by definition), then BC = AE = 11cm; AD = AE + ED = 6 + 11 = 17cm.

The middle line of the trapezoid is 1/2 (BC + AD) = 1/2 (11 + 17) = 14cm.

2) Perimeter ECD = 21cm = ED + CE + CD, then CE + CD = 21 – 6 = 15cm, from point 1 we get that CE = AB (according to the parallelogram), it means AB + CD = 15cm, hence the perimeter trapezium ABCD = 15 + 28 = 43cm.

Answer: The length of the middle line of the trapezoid is 17cm; perimeter ABCD = 43cm.