# Triangular prism

Calculate the surface of a triangular prism 10 cm high, the base of which is a triangle with sides 6 cm 8 cm and 8 cm

Result

S =  264.497 cm2

#### Solution:

$h=10 \ \text{cm} \ \\ a=6 \ \text{cm} \ \\ b=8 \ \text{cm} \ \\ c=8 \ \text{cm} \ \\ o=a+b+c=6+8+8=22 \ \text{cm} \ \\ s=o/2=22/2=11 \ \text{cm} \ \\ S_{1}=\sqrt{ s \cdot \ (s-a) \cdot \ (s-b) \cdot \ (s-c) }=\sqrt{ 11 \cdot \ (11-6) \cdot \ (11-8) \cdot \ (11-8) } \doteq 3 \ \sqrt{ 55 } \ \text{cm}^2 \doteq 22.2486 \ \text{cm}^2 \ \\ S=2 \cdot \ S_{1} + o \cdot \ h=2 \cdot \ 22.2486 + 22 \cdot \ 10 \doteq 264.4972 \doteq 264.497 \ \text{cm}^2$

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