The height of the prism is h=2.5 cm.
Given information:
The volume of the prism is [tex]35\rm\; cm^3[/tex].
The base of the prism is a rectangle with sides 4 cm and 7 cm. 4 cm side is the base of the triangular face.
So, the volume of the prim can be written as,
[tex]V=\dfrac{1}{2}4\times h\times 7[/tex]
The value of h can be calculated as,
[tex]V=\dfrac{1}{2}4\times h\times 7\\35=\dfrac{1}{2}4\times h\times 7\\h=\dfrac{35}{14}\\h=\dfrac{5}{2}=2.5[/tex]
Therefore, the height of the prism is h=2.5 cm.
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https://brainly.com/question/16246207
