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The height of the prism with equilateral triangles base is 25cm.if the perimeter of the base of the prism is 18cm,what is its volume

Sagot :

mhanifa

[tex]225\sqrt{3} \ or \ 389.71 \ cm^3[/tex]

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To find the volume of the prism, we need to calculate the area of the base and multiply it by the height of the prism.

Given:

  • Height of the prism h = 25 cm
  • Perimeter of the base P = 18 cm

The base is an equilateral triangle, so each side of the triangle is:

  • 18 cm / 3 = 6 cm

The area of an equilateral triangle is given by the formula:

  • [tex]A=(\sqrt{3} /4)s^2[/tex]

where s is the length of a side.

Substituting s = 6 cm:

  • [tex]A=(\sqrt{3} /4)*6^2=9\sqrt{3}[/tex]

The volume of the prism is the area of the base multiplied by the height:

  • [tex]V=Ah=9\sqrt{3}*25=225\sqrt{3} =389.71\ cm^3[/tex]

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