Triangular prism - regular

The regular triangular prism is 7 cm high. Its base is an equilateral triangle whose height is 3 cm. Calculate the surface and volume of this prism.

Result

V =  36.373 cm3
S =  83.138 cm2

Solution:

v=3 cm h=7 cm  a2=v2+(a/2)2 4a2=4v2+a2 3a2=4v2  a=v⋅ 2/3=3⋅ 2/3≐2 3 cm≐3.4641 cm  S1=34⋅ a2=34⋅ 3.46412≐3 3 cm2≐5.1962 cm2  V=S1⋅ h=5.1962⋅ 7≐21 3≐36.3731≐36.373 cm3v=3 \ \text{cm} \ \\ h=7 \ \text{cm} \ \\ \ \\ a^2=v^2 + (a/2)^2 \ \\ 4a^2=4v^2 + a^2 \ \\ 3a^2=4v^2 \ \\ \ \\ a=v \cdot \ 2/\sqrt{ 3 }=3 \cdot \ 2/\sqrt{ 3 } \doteq 2 \ \sqrt{ 3 } \ \text{cm} \doteq 3.4641 \ \text{cm} \ \\ \ \\ S_{1}=\dfrac{ \sqrt{ 3 } }{ 4 } \cdot \ a^2=\dfrac{ \sqrt{ 3 } }{ 4 } \cdot \ 3.4641^2 \doteq 3 \ \sqrt{ 3 } \ \text{cm}^2 \doteq 5.1962 \ \text{cm}^2 \ \\ \ \\ V=S_{1} \cdot \ h=5.1962 \cdot \ 7 \doteq 21 \ \sqrt{ 3 } \doteq 36.3731 \doteq 36.373 \ \text{cm}^3
o=3⋅ a=3⋅ 3.4641≐6 3 cm≐10.3923 cm  S=2⋅ S1+o⋅ h=2⋅ 5.1962+10.3923⋅ 7≐48 3≐83.1384≐83.138 cm2o=3 \cdot \ a=3 \cdot \ 3.4641 \doteq 6 \ \sqrt{ 3 } \ \text{cm} \doteq 10.3923 \ \text{cm} \ \\ \ \\ S=2 \cdot \ S_{1} + o \cdot \ h=2 \cdot \ 5.1962 + 10.3923 \cdot \ 7 \doteq 48 \ \sqrt{ 3 } \doteq 83.1384 \doteq 83.138 \ \text{cm}^2

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Hola Qomo Estas
hola qomo estas ya se que esta mal escrito

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