A straight line is drawn through the apex M of the CMR trapezium (larger base-CT), parallel to the lateral side

A straight line is drawn through the apex M of the CMP trapezium (larger base-CT), parallel to the lateral side of the PT. This line and the base of the CT intersect at point E. The perimeter of the triangle KME is 17 cm, MP = 7 cm, KE = 4 cm. Calculate: a) the length of the midline of the trapezoid; b) the perimeter of the trapezoid

In the quadrangle EMPT MP is parallel to ET, since ET lies on the lower base of the CT trapezoid, and ME is parallel to PT by construction, then EMPT is a parallelogram, which means ME = PT, ET = MP = 7 cm.

Base KP = KE + ET = 4 + 7 = 11 cm.

Let’s define the middle line of the trapezoid.

AB = (MR + CT) / 2 = (7 + 11) / 2 = 9 cm.

The perimeter of the trapezoid is: P = (KM + MR + RT + CT).

Since PT = ME, and KT = KE + ET, then P = (KM + ME + KE + MP + ET) = Pkm + 2 * MP = 17 + 14 = 31 cm.

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

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