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Pp=1/2*(8√3)²=1/2*64*3=96 cm²
H=1/2*8=4 cm
V=1/3*Pp*H
V=1/3*96*4=32*4=128 cm³
kąt α = 60°
h - wysokość ostrosłupa = ?
h/b = cosα = 1/2
h = b * 1/2 = 8* 1/2 = 4 cm
d - przekątna podstawy = ?
(d/2) : b = sin60° = √3/2
d/2 = b * √3/2 = 8√3/2 = 4√3 cm
d = 2 * 4√3 = 8√3 cm
a - krawędź podstawy = ?
a√2 = d
a = d/√2 = d√2/2 = 8√3 * √2/2 = 4√6 cm
Pp - pole podstawy = a² = (4√6)² = 16 * 6 = 96 cm²
V - objetośc = 1/3 * Pp * h = 1/3 * 96 cm² * 4 cm = 32 cm³ * 4 cm = 128 cm³