# Triangular prism

The base of the perpendicular triangular prism is a rectangular triangle with a hypotenuse of 10 cm and one leg of 8 cm. The prism height is 75% of the perimeter of the base. Calculate the volume and surface of the prism.

Correct result:

V =  432 cm3
S =  480 cm2

#### Solution:

$c=10 \ \text{cm} \ \\ a=8 \ \text{cm} \ \\ b=\sqrt{ c^2-a^2 }=\sqrt{ 10^2-8^2 }=6 \ \text{cm} \ \\ \ \\ o=a+b+c=8+6+10=24 \ \text{cm} \ \\ h=\dfrac{ 75 }{ 100 } \cdot \ o=\dfrac{ 75 }{ 100 } \cdot \ 24=18 \ \text{cm} \ \\ \ \\ S_{1}=\dfrac{ a \cdot \ b }{ 2 }=\dfrac{ 8 \cdot \ 6 }{ 2 }=24 \ \text{cm}^2 \ \\ \ \\ V=S_{1} \cdot \ h=24 \cdot \ 18=432 \ \text{cm}^3$
$S=2 \cdot \ S_{1} + o \cdot \ h=2 \cdot \ 24 + 24 \cdot \ 18=480 \ \text{cm}^2$

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