Given a pyramid at the base of which lies a rhombus with sides of 4 cm. Acute angles 30 °,

| February 5, 2021 | education

Given a pyramid at the base of which lies a rhombus with sides of 4 cm. Acute angles 30 °, dihedral angles at the base 45 °. Find the volume of the pyramid

Determine the area of the rhombus at the base of the pyramid through two sides and the angle between them.

Savsd = AВ * AD * SinВAD = 4 * 4 * (1/2) = 8 cm2.

Let’s define the area of the rhombus through the side and the height.

Savsd = СD * MН = 4 * MН.

Let’s equate both equations.

4 * MH = 8.

MH = 8/4 = 2 cm.

Then OH = MH / 2 = 2/2 = 1 cm.

Let’s draw the height of the CК of the side face of the pyramid.

In a right-angled triangle KAН, the KНO angle, by condition, is equal to 450, then the KAН triangle is isosceles, KO = OH = 1 cm.

Let’s define the volume of the pyramid.

V = Savsd * KO / 3 = 8 * 1/3 = 2 (2/3) cm3.

Answer: The volume of the pyramid is 2 (2/3) cm3.



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