# 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:

$$\smash{ h = 10 = 10 \ cm \\~\\a = 6 = 6 \ cm \\~\\b = 8 = 8 \ cm \\~\\c = 8 = 8 \ cm \\~\\o = a+b+c = 6+8+8 = 22 \ cm \\~\\s = o/2 = 22/2 = 11 \ cm \\~\\S_{1} = \sqrt{ s \cdot (s-a) \cdot (s-b) \cdot (s-c) } = \sqrt{ 11 \cdot (11-6) \cdot (11-8) \cdot (11-8) } ≐ 22.2486 \ cm^2 \\~\\S = 2 \cdot S_{1} + o \cdot h = 2 \cdot 22.2486 + 22 \cdot 10 = 264.497 \ cm^2 }$$

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