Question

Can someone help me find the surface area, base area, and volume of a regular tetrahedron? With the attachments provided below.

Answer 1

my teacher didnt provide slant height or height so idk how to come up with it

Answer 2

Well she wants us to print out these nets and make them in 3D so idk if when i made them i would have to measure them.

Answer 3

What is the shape of each face?

Answer 4

the faces of a regular tetrahedron are triangles

Answer 5

What kind of triangles? Also, are all faces congruent triangles?

Answer 6

Remember we are dealing with a "regular tetrahedron".

Answer 7

Sorry for the delay, Um acute triangles? or equilaterals? i cant tell and i think all of them are conrgruent

Answer 8

They are all equilateral and congruent triangles.

Answer 9

Oh i see now, so how does that help me with the height and slant height now?

Answer 10

Bisect a face and use pythagoras' theorem.

Answer 11

Would that be for height or slant height?

Answer 12

slant

Answer 13

How do i bisect like im confused

Answer 14

You've created a right angle at the bottom. Use pythagoras' theorem.

The height from a vertex to a face is much harder to picture i think. I'd find the center of the base first, and then use pythagoras theorem with the edge being the hypotenuse and the center of the face being where the right angle is.

Answer 15

Oh ok so for Pyth. Th. i do 5.2^2+?^2=10.4^2

Answer 16

yes

Answer 17

the answer would be 81.12

Answer 18

i think

Answer 19

I'm getting 9.0067.

Answer 20

For the slant height. (10.4^2 - 5.2^2)^.5

Answer 21

oh i forgot to square root.

Answer 22

I have to go now and i hope that when i get on you can still help me :(

Answer 23

I'll go too.

Answer 24

After pythagorean th what should i do?

Answer 25

@iPwnBunnies joel had to leave and so did i so yeah i only started getting help :/

Answer 26

Ok, so we're finding the height of one of the triangles via Pythagorean Theorem. We found it to be approx. 9 units.
So, can you find the area of one whole triangle, then?

Answer 27

Ooo, I'm not sure what slant height is tbh ._.
I don't wanna mess you up.

Answer 28

let me try to search it on the internet and share it with you cuz if i cant be helped ill faint

Answer 29

http://www.mathalino.com/reviewer/solid-mensuration-solid-geometry/regular-tetrahedron

Answer 30

Err, I'm still not sure what's going on. But we can find the area of one whole triangle.
Area of a triangle = 0.5*base*slant height

Answer 31

What will the area help with?

Answer 32

The surface area of the entire tetrahedron.

Answer 33

I take so long cuz my OS is acting weird.......so you dont know slant height and i dont think we have the base either

Answer 34

We do have the base. It's the base of the triangle. And all 4 triangle bases make a square base of the tetrahedron.

Answer 35

its actually a triangle base

Answer 36

Oh crap, yeah, this is a tetrahedron. Then, the area of the base is the same area as one of the sides.
Since we found the area of one side, multiply it by 4 to find the total surface area.

Answer 37

Wait when did we find the area of one side? that was the pythagorean th??

Answer 38

no wait stupid question let me see if i can even find the area by myself

Answer 39

We had to use Pythagorean Theorem to find the slant height of one of the sides. Which we can use to find the area of one side. Then multiply by 4 to get the total surface area

Answer 40

Why do we multiply by four?