Question

Find the surface area?? PLEASE HELP!!

Answer 1

can you find the area of the base?

Answer 2

the surface area of the whole thing is the area of the base plus 6* the area of one of those triangular faces

Answer 3

was it 4?

Answer 4

the area of the base? no. do you see the pair of little right triangles marked off in a section of the base?

Answer 5

what is the base of such a triangle, and the height?

Answer 6

2 square root 3

Answer 7

that's the height. what is the base?

Answer 8

6

Answer 9

those are the only numbers im left with

Answer 10

no. look at the diagram more carefully.

Answer 11

is it 24??

Answer 12

no guessing allowed. you can figure this out.

Answer 13

im not guessing. 4 * 6 is 24

Answer 14

no i cant..thats why im asking for help. :/

Answer 15

what are you trying to compute with 4*6?

Answer 16

to get the base.

Answer 17

okay, we're having a failure to communicate here because base gets used in different contexts.

The base of the pyramid is a hexagon, right? That hexagon has a (what looks like) equilateral triangle drawn in it. That equilateral triangle has two right triangles in it. We are trying to find the area of the base of the pyramid, which is equal to the area of 6 of the "equilateral" triangles or 12 of the smaller triangles. To find the area of the triangles, we need to find their base, which is either the length of the side of the base of the pyramid (for the equilateral triangle) or half the length of the side of the base of the pyramid.

Are we clear on what we're talking about now? :-)

Answer 18

we know the height of those triangles is 2 sqrt(3), and we know the area of a triangle is 1/2 * b * h, so we just need to find b.

Answer 19

your choice on which triangle you want to use :-)

Answer 20

right. think so.. which triangle?

Answer 21

arent they all the same?

Answer 22

no, the equilateral triangle is twice the side of the right triangle!

Answer 23

aannddd..im lost again..

Answer 24

Could you just tell me what formula im missing? or need to use..?

Answer 25

now, do you want to find the area of the right triangle (we'll have 12 of those) or the bigger triangle (we'll have 6 of those)?

Answer 26

either way works. we still need to find the edge length of the base of the pyramid from looking at the diagram with our best Sherlock Holmes impression...

Answer 27

look over at the left side of the diagram...I see a measurement...what is it?

Answer 28

i cant find the base. ive already tried 6* 2 sq. rt 3 ?

Answer 29

please. look at the diagram. what do you see? there are 3 measurements provided. what are they, and what do they measure?

Answer 30

i have been looking. 4 ft is the side. 6 is the height and idk what 2/3 is called.

Answer 31

4 ft is which side? please, be as precise as possible. Pretend I can't actually see the diagram :-)

Answer 32

its just one of the sides.

Answer 33

all the sides equal 4ft,.

Answer 34

it's the 4 I'm concerned with here.

which side? describe what side it is. Is it one of the sides going to the tip of the pyramid? is it a side of the base? what?

Answer 35

some of the sides = 4, some of the sides = 6.

Answer 36

why doesnt 4 equal all of the sides? they all look equal to me

Answer 37

then what is that thing with a 6 next to it?

Answer 38

the height

Answer 39

no, it's not. it's the length of one of the sides going up to the point.
it may seem like I'm giving you a hard time, and should just give you the formula already, but a) you need to understand how to find the formula and b) you won't be able to use the formula successfully if you can't identify which dimension goes where in the formula.

Answer 40

ive googled to formula. its not helping. thats why i asked.

Answer 41

right. trust me, you'll end up understanding :-)

just a sec, I'm drawing a picture in another program.

Answer 42

i probably wont.. but seeing as i have to leave soon anyways why not..?

Answer 43

Here is the diagram with some of the confusion stripped away.

Answer 44

That is only the base of the pyramid.

Answer 45

so theres 6 parts, all of them equal 4.

Answer 46

To find the area of those right triangles, we have the height, 2 sqrt(3), but we need their base length. Notice that 4 ft over on the left. That is the side length of the hexagon which forms the base. The 6 sides of the base are identical, but there are 6 other sides on the pyramid, each of which is 6 ft, not 4 ft. That's why I was being a stickler.

Now, can you find the area of either the equilateral (maybe) triangle, of which there are 6, or the right triangle, of which there are 12?

I have no idea what you mean by "6 parts, all of them equal 4" There are 6 sides to the hexagon, all of which are 4 ft in length.

Answer 47

ok

Answer 48

So, what is the length of the bottom side (the one running parallel to the bottom of the diagram)? that's 4 ft, right? so the base length of the right triangle is 1/2 of 4 ft, or 2 ft. the base length of the bigger triangle is 4 ft. What is the area of the right or bigger triangle (pick one, and answer)?

Answer 49

idk. im confused.

Answer 50

what is the area?

Answer 51

you mean, 2 * 2/3 ??

Answer 52

\[A = \frac{1}{2}bh\]

Answer 53

6.9

Answer 54

Please, you want to keep answers in symbolic form for as long as possible.

Answer 55

what do you mean symbolic form?

Answer 56

Yes, \(4\sqrt{3} \approx 6.9\) but no, that is not the area of that triangle. Look at my formula again.

keep the square root sign, pi, etc. instead of having things like 6.9 (which are also inexact, because the square root of 3 is irrational and so has an infinite number of digits)

Answer 57

ok?

Answer 58

\[h = 2\sqrt{3}\]\[b = 2\]\[A = \frac{1}{2}bh = \frac{1}{2}(2)(2\sqrt{3}) = \]

Answer 59

a= 1/2 2* 2/3