At the base of the pyramid there is a triangle (6; 8: 10). The side faces are inclined to the base

| May 26, 2021 | education

At the base of the pyramid there is a triangle (6; 8: 10). The side faces are inclined to the base at an angle of 45` find Sб; V (24√2; 16)

Since AC ^ 2 = AB ^ 2 + BC ^ 2, the triangle ABC is rectangular. The side faces of the pyramid are inclined at an angle of 45, then the apex of the pyramid is projected to the center of the inscribed circle, and all apothems have the same length.

Savs = AB * BC / 2 = 8 * 6/2 = 24 cm2.

The semi-perimeter ABC is equal to: p = (10 + 8 + 6) / 2 = 12 cm.

Then r = OH = S / p = 24/12 = 2 cm.

The triangle DOH is rectangular and isosceles, since the angle ОНD = 45, then ОD = ОН = 2 cm, DH = 2 * √2 cm.

Side = (AC + AB + BC) * DH / 2 = 24 * 2 * √2 / 2 = 24 * √2 cm2.

V = Sosn * OD / 3 = 24 * 2/3 = 16 cm3.

Answer: The area of the side face is 24 * √2 cm2, the volume is 16 cm3.



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