Triangular prism

Calculate a triangular prism if it has a rectangular triangle base with a = 4cm and hypotenuse c = 50mm, and the height of the prism is 0.12 dm.

Correct answer:

V =  7.2 cm³
S =  26.4 cm²

Step-by-step explanation:

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

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

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