Side edges

The regular 4-sided pyramid has a body height of 2 dm, and the opposite side edges form an angle of 70°.
Calculate the surface area and volume of the pyramid.

Correct answer:

S =  12.7621 dm2
V =  2.6149 dm3

Step-by-step explanation:

h=2 dm α=70° rad=70° 180π =70° 1803.1415926 =1.22173=7π/18 θ=α/2=1.2217/20.6109 rad tanθ=u/2:h  u=2 h tanθ=2 2 tan0.61092.8008 dm u2=a2+a2 a=u/2=2.8008/21.9805 dm  h2=h2+(a/2)2=22+(1.9805/2)22.2317 dm  S1=a2=1.980523.9223 dm2 S2=2a h2=21.9805 2.23172.2099 dm2  S=S1+4 S2=3.9223+4 2.2099=12.7621 dm2
V=31 S1 h=31 3.9223 2=2.6149 dm3

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See also our trigonometric triangle calculator.

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