Calculate a prism

Calculate the volume and surface area of a prism whose height is 16cm and whose base is a right triangle with sides of 5cm and 12cm and a hypotenuse of 13cm.

Final Answer:

V =  480 cm³
S =  540 cm²

Step-by-step explanation:

$$\begin{gathered} h=16\text{cm} \\ a=5\text{cm} \\ b=12\text{cm} \\ c=13\text{cm} \\ {S}_1=\frac{a\cdot b}{2}=\frac{5\cdot 12}{2}=30{\text{cm}}^2 \\ V=S_1\cdot h=30\cdot 16=480{\text{cm}}^3 \end{gathered}$$

$$\begin{gathered} S_2=(a+b+c)\cdot h=(5+12+13)\cdot 16=480{\text{cm}}^2 \\ S=2\cdot S_1+S_2=2\cdot 30+480=540{\text{cm}}^2 \end{gathered}$$

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