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.

Correct answer:

V =  7.2 cm³
S =  26.4 cm²

Step-by-step explanation:

$$\begin{gathered} a=4\text{ cm } \\ c=50\text{ mm}\to \text{ cm}=50\mathrm{/}10\text{ cm}=5\text{ cm } \\ h=0.12\text{ dm}\to \text{ cm}=0.12\cdot 10\text{ cm}=1.2\text{ cm } \\ b=\sqrt{c^2-a^2}=\sqrt{5^2-4^2}=3\text{ cm } \\ {S}_1={\displaystyle \frac{a\cdot b}{2}}={\displaystyle \frac{4\cdot 3}{2}}=6{\text{cm}}^2 \\ V=S_1\cdot h=6\cdot 1.2={\displaystyle \frac{36}{5}}={\displaystyle \frac{36}{5}}{\text{cm}}^3=7.2{\text{cm}}^3 \end{gathered}$$

$$\begin{gathered} o=a+b+c=4+3+5=12\text{ cm } \\ S=2\cdot S_1+o\cdot h=2\cdot 6+12\cdot 1.2={\displaystyle \frac{132}{5}}={\displaystyle \frac{132}{5}}{\text{cm}}^2=26.4{\text{cm}}^2 \end{gathered}$$

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