# The base of the pyramid is an isosceles trapezoid, in which the lengths of the parallel sides are 2 and 8 cm.

The base of the pyramid is an isosceles trapezoid, in which the lengths of the parallel sides are 2 and 8 cm. Calculate the volume of the pyramid if each dihedral angle at the base edge is 60 degrees.

The condition says that the base of the pyramid is an isosceles trapezoid, in which the lengths of the parallel sides are 2 cm and 8 cm. It is also known that each dihedral angle at the base edge is 60 °.

Based on the condition that all dihedral angles at the base edges are equal, then the base of the pyramid’s height is the center of the circle inscribed in the trapezoid.

Let’s calculate the side of the trapezoid as the middle line:

(8 + 2) / 2 = 5 cm.

We find the height by the Pythagorean theorem:

√ (5 ^ 2 – 3 ^ 2) = 4 cm.

Let’s calculate the volume by the formula:

V = 1/3 * S * H ​​= 1/3 * 20 * 2√3 = 40√3 / 3 cm ^ 3;

where H = 2 * tg 60 ° = 2√3;

S = ((2 + 8) / 2) * 4 = 20 cm ^ 2.

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