Triangular prism

Calculate the surface area and volume of a three-sided prism with a base of a right-angled triangle if its sides are a = 3 cm, b = 4 cm, c = 5 cm, and the height of the prism is v = 12 cm.

Correct answer:

S =  156 cm²
V =  72 cm³

Step-by-step explanation:

$$\begin{gathered} a=3\text{cm} \\ b=4\text{cm} \\ c=5\text{cm} \\ v=12\text{cm} \\ {S}_1=\frac{a\cdot b}{2}=\frac{3\cdot 4}{2}=6{\text{cm}}^2 \\ o=a+b+c=3+4+5=12\text{cm} \\ S=2\cdot S_1+o\cdot v=2\cdot 6+12\cdot 12=156{\text{cm}}^2 \end{gathered}$$

$V=S_1\cdot v=6\cdot 12=72{\text{cm}}^3$

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