The base of the pyramid is a rhombus with a side of 10cm and a height of 6cm.

| March 6, 2021 | education

The base of the pyramid is a rhombus with a side of 10cm and a height of 6cm. Find the volume of the pyramid if all dihedral angles at its base are 45 degrees.

Since the dihedral angles at the base of the pyramid are equal, the apex point of the pyramid, point P, is projected to the center of the inscribed circle, which is the intersection point of the diagonals.

The segment PH is the perpendicular to CD, the segment OH is the projection of the PH on the plane of the rhombus, then OH is perpendicular to the CD, and the linear angle OHP is the dihedral angle at the base.

Then, in a right-angled triangle OРН, the angle OHP = 45, which means that the triangle is isosceles, OH = OP.

The segment OH is half the height of the MH of the rhombus ABCD, then OH = OP = MH / 2 = 6/2 = 3 cm.

Determine the area of ​​the base of the pyramid.

Savsd = CD * MН = 10 * 6 = 60 cm2.

Then V = Sosn * PO / 3 = 60 * 3/3 = 60 cm3.

Answer: The volume of the pyramid is 60 cm3.



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