Prism

Calculate the volume of the rhombic prism. The prism base is a rhombus whose one diagonal is 47 cm, and the edge of the base is 27 cm. The edge length and height of the base of the prism are 4:3.

Final Answer:

V =  12653.3 cm³

Step-by-step explanation:

$$\begin{gathered} a=27\text{cm} \\ u=47\text{cm} \\ r=4:3=a:h \\ h=\frac{3}{4}\cdot a=\frac{3}{4}\cdot 27=\frac{3\cdot 27}{4}=\frac{81}{4}=20.25\text{cm} \\ s=\frac{a+a+u}{2}=\frac{27+27+47}{2}=\frac{101}{2}=50.5\text{cm} \\ {S}_1=\sqrt{s\cdot (s-a)\cdot (s-a)\cdot (s-u)}=\sqrt{50.5\cdot (50.5-27)\cdot (50.5-27)\cdot (50.5-47)}\doteq 312.4263{\text{cm}}^2 \\ V=2\cdot S_1\cdot h=2\cdot 312.4263\cdot 20.25=12653.3{\text{cm}}^3 \end{gathered}$$

Try another example