In the trapezoid ABCD, the lateral sides AB = 13 cm, CD = 15 cm. The perimeter is 48 cm.

In the trapezoid ABCD, the lateral sides AB = 13 cm, CD = 15 cm. The perimeter is 48 cm. Find the middle line of the trapezium MK.

The middle line is the segment that connects the midpoints of the sides of the trapezoid.

In order to calculate the middle line, you need to divide the sum of its bases by two:

MH = (BC + AD) / 2.

The perimeter of a trapezoid is the sum of all its sides:

P = AB + BC + CD + AD.

Since we know the perimeter of this trapezoid and the length of its lateral sides, then:

BC + AD = P – (AB + CD);

BC + AD = 48 – (13 + 15);

ВС + АD = 48 – 28 = 20 cm.

MH = 20/2 = 10 cm.

Answer: The middle line of the trapezoid is 10 cm.