Question

Find the volume and total surface area of a regular tetrahedron whose measure of one edge is 10cm

Answer 1

do you know the formulaes for the surface area of a tetrahedron?

Answer 2

I assume not so here it is:
\[\sqrt{3} a ^{2}\]

Answer 3

@bozybosman then you multiply that to 4 right to get the total surface area?

Answer 4

cry

Answer 5

there is different ways you can find the surface area and the volume
1. find the base plane are which is [(Sq root 3 ) /4 ] a^2 a= to the edge length
2. find the surface area which is 4( base plane area) or (Sq root 3) a^2
3. To find the volume you can use the formula V= [(Sq root 2) / 12] a^3

I hope this helps

Answer 6

no so that is the formula for surface area you can derive it from the surface area for a right angled triangle. the formula for the surface area of a single face is:
\[\frac{ \sqrt{3} }{ 4 }a ^{2}\]

Answer 7

1) V = 1/12 (a^3) x 3^(1/2)
= 1/12 ( 10^3) x 3^(1/2)
= 1000/12 x 3^(1/2)
= 144.338 cm^3 (3 dec.plcs)

Answer 8

how about the Total surface area?

Answer 9

Total surface area is:\[Total Surface Area =\frac{\sqrt{3}}{4}a^2\]

Answer 10

a is the apothem? or the edge?

Answer 11

a is the edge because this is a regular tetrahedron it is the same for all sides