The middle line of an equilateral triangle with a side of 6 cm divides it into a triangle

The middle line of an equilateral triangle with a side of 6 cm divides it into a triangle and a quadrangle. Determine the kind of quadrilateral and find its perimeter.

Since the triangle ABC is equilateral, then AB = BC = AC = 6 cm.The middle line of the triangle is equal to half the length of the side parallel to it, then KP = AC / 2 = 6/2 = 3 cm.

Points K and P divide the segments AB and BC in half, then AK = CP = 6/2 = 3 cm.

The middle line KR of the ABC triangle divides it into an equilateral triangle KВР and an isosceles trapezoid AKРС, the perimeter of which is equal to: Rakrs = AK + KР + РС + AC = 3 + 3 + 3 + 6 = 15 cm.

Answer: A quadrilateral is an isosceles trapezoid. The perimeter of the trapezoid is 15 cm.