Pyramid a+h

Calculate the volume and surface area of the pyramid on the edge and height a = 26 cm. h = 3 dm.

Result

S =  2376.169 cm2
V =  6760 cm3

Solution:

a=26 cm v=3⋅ 10=30 cm S1=a2=262=676 cm2 h2=v2+(a/2)2=302+(26/2)2=1069 cm≐32.6956 cm S2=a⋅ h2/2=26⋅ 32.6956/2=13 1069 cm2≐425.0424 cm2 S=S1+4⋅ S2=676+4⋅ 425.0424≐2376.1694=2376.169 cm2a = 26 \ cm \ \\ v = 3 \cdot \ 10 = 30 \ cm \ \\ S_{ 1 } = a^2 = 26^2 = 676 \ cm^2 \ \\ h_{ 2 } = \sqrt{ v^2 + (a/2)^2 } = \sqrt{ 30^2 + (26/2)^2 } = \sqrt{ 1069 } \ cm \doteq 32.6956 \ cm \ \\ S_{ 2 } = a \cdot \ h_{ 2 }/2 = 26 \cdot \ 32.6956/2 = 13 \ \sqrt{ 1069 } \ cm^2 \doteq 425.0424 \ cm^2 \ \\ S = S_{ 1 }+4 \cdot \ S_{ 2 } = 676+4 \cdot \ 425.0424 \doteq 2376.1694 = 2376.169 \ cm^2
V=S1⋅ v/3=676⋅ 30/3=6760=6760 cm3V = S_{ 1 } \cdot \ v/3 = 676 \cdot \ 30/3 = 6760 = 6760 \ cm^3

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