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The length of an edge of a regular tetrahedron is $8cm$. Find the total area of surfaces and the volume

I've been able to find the area of all surfaces, which is $(4\times27.713) cm^2$ but I'm not able to find the volume.

There's no height given. How can I derive the height?

Blue
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tryingtobeastoic
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2 Answers2

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Hint

the heights in the base are crossing each other in the ratio $1:2$ exactly under the top.

Jaroslaw Matlak
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The volume of a regular tetrahedron with side $a$ is given by

$V = \frac {a^3} {6 \sqrt{2}}$

Weather Vane
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  • @Brahadeesh it answers the Y part of an XY question. The problem is "Find the total area of surfaces and the volume". – Weather Vane Sep 19 '18 at 08:46
  • fair enough... but a little more explanation would help improve the answer. The OP wants to know about the height of a tetrahedron given the side length. –  Sep 19 '18 at 08:48
  • @Brahadeesh it's a possible duplicate question anyway, please see my comment below the question. – Weather Vane Sep 19 '18 at 09:04
  • thank you for searching it out, I’ve added my vote to close as duplicate based on the link. –  Sep 19 '18 at 09:06