Diamond prism

The prism's base is a diamond with a side length of 6 cm and a height of 4 cm. The height of the prism is 125% greater than the length of the side of the diamond. Calculate the surface area and volume of the prism.

Final Answer:

S =  372 cm²
V =  324 cm³

Step-by-step explanation:

$$\begin{gathered} a=6 \\ {h}_1=4 \\ {h}_2=a+1.25\cdot a=6+1.25\cdot 6=\frac{27}{2}=13.5 \\ {S}_1=a\cdot h_1=6\cdot 4=24 \\ o=4\cdot a=4\cdot 6=24 \\ {S}_2=o\cdot h_2=24\cdot 13.5=324 \\ S=2\cdot S_1+S_2=2\cdot 24+324=372{\text{cm}}^2 \end{gathered}$$

$V=S_1\cdot h_2=24\cdot 13.5=324{\text{cm}}^3$

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