Perpendicular 3482

The lengths of the base legs are 7.2 cm and 4.7 cm, and the height of the prism is 24 cm. Calculate the volume and surface of a triangular perpendicular prism with the base of a right triangle.

Correct answer:

V =  406.08 cm³
S =  525.7981 cm²

Step-by-step explanation:

$$\begin{gathered} a=7.2\text{cm} \\ b=4.7\text{cm} \\ h=24\text{cm} \\ c=\sqrt{a^2+b^2}=\sqrt{7.2^2+4.7^2}\doteq 8.5983\text{cm} \\ {S}_1=a\cdot b/2=7.2\cdot 4.7/2=\frac{423}{25}=16.92{\text{cm}}^2 \\ V=S_1\cdot h=16.92\cdot 24=406.08{\text{cm}}^3 \end{gathered}$$

$S=2\cdot S_1+(a+b+c)\cdot h=2\cdot 16.92+(7.2+4.7+8.5983)\cdot 24=525.7981{\text{cm}}^2$

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