Answer :
[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]
