Quadrangular pyramid

Calculate the surface area and volume of a regular quadrangular pyramid:
sides of bases (bottom, top): a1 = 18 cm, a2 = 6cm
angle α = 60 ° (Angle α is the angle between the sidewall and the base plane.)
S =? , V =?

Correct answer:

h =  10.3923 cm
S =  936 cm2
V =  1621.2 cm3

Step-by-step explanation:

a1=18 cm a2=6 cm A=60   S1=a12=182=324 cm2 S2=a22=62=36 cm2 t=tanA°=tan60° =1.732051=1.73205 b1=a1/2=18/2=9 cm b2=a2/2=6/2=3 cm  h1=b1 t=9 1.7321=9 3 cm15.5885 cm h2=b2 t=3 1.7321=3 3 cm5.1962 cm  h3=h12+b12=15.58852+92=18 cm h4=h22+b22=5.19622+32=6 cm  h=h1h2=15.58855.1962=6 3=10.3923 cm
S3=a1 h3/2=18 18/2=162 cm2 S4=a2 h4/2=6 6/2=18 cm2 S=4 (S3S4)+S1+S2=4 (16218)+324+36=936 cm2
V=h/3 (S1+S1 S2+S2)=10.3923/3 (324+324 36+36)=936 3=1621.2 cm3

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See also our trigonometric triangle calculator.

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