Rhombus base

Calculate the volume and surface area of prisms whose base is a rhombus with diagonals u₁ = 17 cm and u₂ = 14 cm. The prism height is twice the base edge length.

Final Answer:

V =  2620.7 cm³
S =  1208 cm²

Step-by-step explanation:

$$\begin{gathered} u_1=17\text{cm} \\ {u}_2=14\text{cm} \\ (u_1/2{)}^2+(u_2/2{)}^2=a^2 \\ a=\sqrt{(u_1/2{)}^2+(u_2/2{)}^2}=\sqrt{(17/2{)}^2+(14/2{)}^2}\doteq 11.0114\text{cm} \\ {S}_1=\frac{u_1\cdot u_2}{2}=\frac{17\cdot 14}{2}=119{\text{cm}}^2 \\ h=2\cdot a=2\cdot 11.0114=\sqrt{485}\text{cm}\doteq 22.0227\text{cm} \\ V=S_1\cdot h=119\cdot 22.0227=119\sqrt{485}=2620.7{\text{cm}}^3 \end{gathered}$$

$$\begin{gathered} o=4\cdot a=4\cdot 11.0114=2\sqrt{485}\text{cm}\doteq 44.0454\text{cm} \\ {S}_2=o\cdot h=44.0454\cdot 22.0227=970{\text{cm}}^2 \\ S=2\cdot S_1+S_2=2\cdot 119+970=1208{\text{cm}}^2 \end{gathered}$$

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