Quadrilateral 83421

Calculate the volume of the shell of a quadrilateral prism with a rhombus-shaped base with dimensions a=6cm, va=40mm. The height of the prism is 81 mm.

Correct answer:

P =  242.4 cm²

Step-by-step explanation:

$$\begin{gathered} a=6\text{cm} \\ v=40\text{mm}\to \text{cm}=40:10\text{cm}=4\text{cm} \\ h=81\text{mm}\to \text{cm}=81:10\text{cm}=8.1\text{cm} \\ {S}_1=4\cdot a\cdot h=4\cdot 6\cdot 8.1=\frac{972}{5}=194.4{\text{cm}}^2 \\ {S}_2=a\cdot v=6\cdot 4=24{\text{cm}}^2 \\ P=S_1+2\cdot S_2=194.4+2\cdot 24=242.4{\text{cm}}^2 \end{gathered}$$

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