Base diagonal

In a regular 4-sided pyramid, the side edge forms an angle of 55° with the base's diagonal. The length of the side edge is eight meters. Calculate the surface area and volume of the pyramid.

Correct answer:

S =  137.0161 m2
V =  91.9869 m3

Step-by-step explanation:

s=8 m φ=55° rad=55° 180π =55° 1803.1415926 =0.95993=11π/36  sinφ=h:s h=s sinφ=8 sin0.95996.5532 m  cosφ=u/2:s  u=2 s cosφ=2 8 cos0.95999.1772 m u2=a2+a2 a=u/2=9.1772/26.4893 m  h2=h2+(a/2)2=6.55322+(6.4893/2)27.3125 m  S1=a2=6.4893242.1107 dm2 S2=2a h2=26.4893 7.312523.7263 m2  S=S1+4 S2=42.1107+4 23.7263=137.0161 m2
V=31 S1 h=31 42.1107 6.5532=91.9869 m3

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