4side pyramid

Calculate the volume and surface of 4 sides regular pyramid whose base edge is 4 cm long. The angle from the plane of the sidewall and base plane is 60 degrees.

Result

V =  18.47 cm3
S =  48 cm2

Solution:

a=4 cm h=(a/2)tan60=3.464 cm h2=h2+(a/2)2=4 cm  V=13a2h=18.47 cm3a = 4 \ cm \ \\ h = (a/2) \cdot \tan 60 ^\circ = 3.464 \ cm \ \\ h_2 = \sqrt{ h^2 + (a/2)^2 } = 4 \ cm \ \\ \ \\ V = \dfrac13 a^2 h = 18.47 \ \text{cm}^3
S1=ah2/2=8 S=4S1+a2=48 cm2S_1 = a h_2 / 2 = 8 \ \\ S = 4 \cdot S_1 + a^2 = 48 \ \text{cm}^2



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