Find the

Find the volume and surface of a prism with a height of 120 mm, the base of which is a right isosceles triangle with a leg length of 5 cm.

Correct answer:

V =  150 cm³
S =  229.8528 cm²

Step-by-step explanation:

$$\begin{gathered} h=120\text{mm}\to \text{cm}=120:10\text{cm}=12\text{cm} \\ a=5\text{cm} \\ b=5\text{cm} \\ {c}^2=a^2+b^2 \\ {S}_1=\frac{a\cdot b}{2}=\frac{5\cdot 5}{2}=\frac{25}{2}=12.5{\text{cm}}^2 \\ V=S_1\cdot h=12.5\cdot 12=150{\text{cm}}^3 \end{gathered}$$

$$\begin{gathered} c=\sqrt{2}\cdot a=\sqrt{2}\cdot 5=5\sqrt{2}\text{cm}\doteq 7.0711\text{cm} \\ {S}_2=h\cdot (a+b+c)=12\cdot (5+5+7.0711)\doteq 204.8528{\text{cm}}^2 \\ S=2\cdot S_1+S_2=2\cdot 12.5+204.8528=229.8528{\text{cm}}^2 \end{gathered}$$

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