# Vertical prism

The base of vertical prism is a right triangle with leg a = 5 cm and a hypotenuse c = 13 cm. The height of the prism is equal to the circumference of the base. Calculate the surface area and volume of the prism

Result

S =  960 cm2
V =  900 cm3

#### Solution:

$a=5 \ \\ c=13 \ \\ b=\sqrt{ c^2-a^2 }=\sqrt{ 13^2-5^2 }=12 \ \\ h=a+b+c=5+12+13=30 \ \\ P=a \cdot \ b/2=5 \cdot \ 12/2=30 \ \\ S=2 \cdot \ P + a \cdot \ h+b \cdot \ h+c \cdot \ h=2 \cdot \ 30 + 5 \cdot \ 30+12 \cdot \ 30+13 \cdot \ 30=960 \ \text{cm}^2$
$V=P \cdot \ h=30 \cdot \ 30=900 \ \text{cm}^3$

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