Right-angled triangle base

Find the volume and surface area of a triangular prism with a right-angled triangle base if the length of the prism base legs are 7.2 cm and 4.7 cm and the height of the prism is 24 cm.

Final Answer:

V =  406.08 cm³
S =  525.7981 cm²

Step-by-step explanation:

$$\begin{gathered} a=7.2\text{cm} \\ b=4.7\text{cm} \\ h=24\text{cm} \\ {S}_1=\frac{a\cdot b}{2}=\frac{7.2\cdot 4.7}{2}=\frac{423}{25}=16.92{\text{cm}}^2 \\ V=S_1\cdot h=\frac{423}{25}\cdot 24=\frac{423\cdot 24}{25}=\frac{10152}{25}=\frac{10152}{25}{\text{cm}}^3=406.08{\text{cm}}^3 \end{gathered}$$

$$\begin{gathered} c^2=a^2+b^2 \\ c=\sqrt{a^2+b^2}=\sqrt{7.2^2+4.7^2}\doteq 8.5983\text{cm} \\ p=a+b+c=7.2+4.7+8.5983\doteq 20.4983\text{cm} \\ S=2\cdot S_1+p\cdot h=2\cdot 16.92+20.4983\cdot 24=525.7981{\text{cm}}^2 \end{gathered}$$

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