# Triangular prism

Calculate a triangular prism if it has a rectangular triangle base with a = 4cm and hypotenuse c = 50mm and height of the prism is 0.12 dm.

Result

V =  7.2 cm3
S =  26.4 cm2

#### Solution:

$a=4 \ \text{cm} \ \\ c=50 \ mm=50 / 10 \ cm=5 \ cm \ \\ h=0.12 \ dm=0.12 \cdot \ 10 \ cm=1.2 \ cm \ \\ \ \\ b=\sqrt{ c^2-a^2 }=\sqrt{ 5^2-4^2 }=3 \ \text{cm} \ \\ \ \\ S_{1}=\dfrac{ a \cdot \ b }{ 2 }=\dfrac{ 4 \cdot \ 3 }{ 2 }=6 \ \text{cm}^2 \ \\ \ \\ V=S_{1} \cdot \ h=6 \cdot \ 1.2=\dfrac{ 36 }{ 5 }=7.2 \ \text{cm}^3$
$o=a+b+c=4+3+5=12 \ \text{cm} \ \\ \ \\ S=2 \cdot \ S_{1} + o \cdot \ h=2 \cdot \ 6 + 12 \cdot \ 1.2=\dfrac{ 132 }{ 5 }=26.4 \ \text{cm}^2$

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