DABC – Regular pyramid. DO perpendicular (ABC), CK perpendicular to AB, AM perpendicular to BC, BM perpendicular

DABC – Regular pyramid. DO perpendicular (ABC), CK perpendicular to AB, AM perpendicular to BC, BM perpendicular to AC. AD = 2√3, ADB angle = 120 degrees. It is necessary to find the P base.

Since the pyramid is regular, there is an equilateral triangle at its base, and the side edges are equal to each other.

AD = BD = CD = 2 * √3 cm.

In an isosceles triangle ABC, by the cosine theorem, we define the side AB.

AB² = DA² + DB² – 2 * DA * DB * cos120 °.

AB² = (2 * √3) ² + (2 * √3) ² – 2 * 2 * √3 * 2 * √3 * (- 1/2).

AB² = 12 + 12 + 12 = 36.

AB = BC = AC = 6 cm.

P = 3 * AB = 3 * 6 = 18 cm.

Answer: the perimeter of the base is 18 cm.