# Hexagonal prism

The base of the prism is a regular hexagon consisting of six triangles with side a = 12 cm and height va = 10.4 cm. The prism height is 5 cm. Calculate the volume and surface of the prism!

Correct result:

V =  1870.615 cm3
S =  1108.246 cm2

#### Solution:

$a=12 \ \text{cm} \ \\ h=5 \ \text{cm} \ \\ o=6 \cdot \ a=6 \cdot \ 12=72 \ \text{cm} \ \\ v=\sqrt{ a^2-(a/2)^2 }=\sqrt{ 12^2-(12/2)^2 } \doteq 6 \ \sqrt{ 3 } \ \text{cm} \doteq 10.3923 \ \text{cm} \ \\ S_{1}=a \cdot \ v/2=12 \cdot \ 10.3923/2 \doteq 36 \ \sqrt{ 3 } \ \text{cm}^2 \doteq 62.3538 \ \text{cm}^2 \ \\ S_{6}=6 \cdot \ S_{1}=6 \cdot \ 62.3538 \doteq 216 \ \sqrt{ 3 } \ \text{cm}^2 \doteq 374.123 \ \text{cm}^2 \ \\ V=S_{6} \cdot \ h=374.123 \cdot \ 5=1080 \ \sqrt{ 3 }=1870.615 \ \text{cm}^3$
$S=2 \cdot \ S_{6} + o \cdot \ h=2 \cdot \ 374.123 + 72 \cdot \ 5=1108.246 \ \text{cm}^2$

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