Respuesta :

roohafzah

Answer :

  • height = 7 m

Explanation :

  • volume = area*height

here,

  • volume = 84 m^3
  • area = 12 m^2

thus, height would be equal to

  • height = 84 m^3/12 m^2
  • height = 7 m

semsee45

Answer:

7 meters

Step-by-step explanation:

To determine the height of a square-based prism given the area of its base and its volume, we can use the formula for the volume of a square-based prism:

[tex]\boxed{\begin{array}{l}\underline{\textsf{Volume of a Square-based Prism}}\\\\V=a \times h\\\\\textsf{where:}\\\phantom{ww}\bullet\;\textsf{$V$ is the volume.}\\\phantom{ww}\bullet\;\textsf{$a$ is the area of the base.}\\\phantom{ww}\bullet\;\textsf{$h$ is the height.}\end{array}}[/tex]

In this case:

  • a = 12 m²
  • V = 84 m³

Substitute the values into the volume formula and solve for h:

[tex]84=12 \times h\\\\\\\dfrac{84}{12}=\dfrac{12h}{12}\\\\\\7=h[/tex]

Therefore, the height of the prism is:

[tex]\LARGE\boxed{\boxed{7\; \rm meters}}[/tex]

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