Question

Find the Total Area of the regular pyramid?
Picture: http://i626.photobucket.com/albums/tt350/nessie_black123/prob4.jpg

Answer 1

Can you find the area of the base?

Answer 2

How would i do that?

Answer 3

would it be 4 x 6??

Answer 4

You have one side on the base already given to you (6) and it is a regular shape, so you have six triangles making up the base. and they are all equilateral which means they have the same shape, and b * h /2 is the area of a triangle and both the b and h are 6.

Answer 5

please tell me if that doesn't make sense.

Answer 6

oh wait, not 4 x 6 i was looking at a different problem. wow. haha.
so if both b and h are 6, do i just plug that in into b * h/2?

Answer 7

Yup and that would give you one triangle of the bottom, and there are six triangles...

Answer 8

so..18?

Answer 9

That would be one triangle on the bottom, and there are 6 triangles that make up the bottom of the shape.

Answer 10

so 6 * 18 would be for the entire base?
108?

Answer 11

Yup!

Answer 12

okay! so now what do i do with that in order to get the total area?

Answer 13

Now you need to get the hypotenuse of the 6 by 8 triangle in order to get the outside base to top length.

Answer 14

so would i use the Pythagorean theorem?

Answer 15

You are correct.

Answer 16

i got 10..

Answer 17

Me too, so now you need to do the same thing as in the first part to get the area of a single outside base to top triangle.

Answer 18

um, how would i do that. same equation?

Answer 19

Yup you still have b * h / 2 but now your b and h are different.

Answer 20

what would be the b and h though??

Answer 21

Do you have a picture? You are trying to find the outside-upper triangles.

Answer 22

this is the only picture i have..

Answer 23

Right, and you found the bottom area by a 6 by 6 triangle, and you found the hypotenuse going from the bottom edge to the top to be 10. So now you need the triangle that is formed from the hypotenuse and the bottom edge.

Answer 24

um.im sort of confused..what triangle?

Answer 25

You are trying to find the area of one of the six triangles that go from the base to the top.

Answer 26

oooh ok. so i use b*h/2 right?
um..would it be 6*10/2??

Answer 27

Yup!

Answer 28

So then how many of those areas are there?

Answer 29

30. would i multiply that by 6?

Answer 30

Yeah, ad then add that to the bottom and you have your answer!

Answer 31

so 180 * 108?

Answer 32

oh wait you said add. so it would be 288?

Answer 33

Yup! :D

Answer 34

okay! But it says that the answer is ( sqrt + sqrt ) and that i need to fill it in..

Answer 35

uhm....

Answer 36

at the bottom of the picture, it shows the part that i have to fill in...

Answer 37

Is this an online class? and I see that now.

Answer 38

yeah. it's odyssey.

Answer 39

You can try
3*sqrt(36) + 18*sqrt(100)
Or can you not do multiplication outside the sqrt signs?

Answer 40

i think that might work..it wont tell me if its right or not until i pass the entire lesson

Answer 41

sorry that answer would be wrong it should be
18*sqrt(36) + 18*sqrt(100)

Answer 42

okay thanks! could you help me with another one?

Answer 43

Sure, I only have another 30 mins though.

Answer 44

ok.

Answer 45

Okay so you have 2 different size triangles that you have to solve for can you tell me what the sides of each of the four triangles are?

Answer 46

um 12 and 10?

Answer 47

Right kind of, do you see that the regular pyramid can be broken up into four triangles?

Answer 48

yeah, like the faces?

Answer 49

Yup, now if you took all the faces apart, what would be each side length of each face?

Answer 50

..12?

Answer 51

or 10...haha idk!

Answer 52

Well there are four different triangles
So one triangle would have side lengths of 12 by 12 by 12 do you see that one?

Answer 53

Yeah, on the bottom, right?

Answer 54

Right, now can try to find the side lengths of the other three triangles?

Answer 55

um, would they be 10,12, and 10?

Answer 56

Yup all three of the other ones would be that!
So now we need to find the area's of them. We can start by the bottom one because that is easier.

Answer 57

ok, so would i just multiply 12 by 3?

Answer 58

That would be finding the perimeter. so no, lemmi think.

Answer 59

You need to use the formula B * H / 2 again, and you have the B but the height we would get by using the 30 60 90 method.

Answer 60

x / 2 * sqrt(3) would be the length of the height where x = 12 (the two non-base sides)

Answer 61

wat.

Answer 62

so 12/2*sqrt of 3 would be my height..?

Answer 63

Yup.

Answer 64

6 sqrt of 3?

Answer 65

Yup. which is about 10.39 but your answer needs square roots so you can leave it like that.

Answer 66

yeah, the thing at the bottom of the picture shows a square root..
so now what do i do?

Answer 67

Now you have to find the area of the three other squares (which are all the same) using the same method we used before.

Answer 68

would 10 be the height?

Answer 69

nope =/ I don't think I know the way that it should be done. I can give you two complicated formulas to do it... but that's probably not the way you are trying to be taught.

Answer 70

There are three triangle with 10, 10 and 12. and I am trying to figure out how to get the height from the 12(base) to the top.

Answer 71

ehhh. i just want to get this crap out of the way haha. as long as i can get it and understand it partially, its all good to me.

Answer 72

Well the complicated way is get the perimeter of the triangle divided by two so (10+10+12)/2 = 16

Answer 73

That is p and then you put it into this formula Area = sqrt(p(p-a)(p-b)(p-c))
p = 16, a = 10, b = 10, & c = 12

Answer 74

And if you do that it comes out to be 48

Answer 75

So now that you have the two different triangles can you tell me what the total area is? (sorry that the formula is complicated, I don't really know how to explain that I just know it works.)

Answer 76

uh. wat. hahahaha

Answer 77

The area to the triangle 10 by 10 by 12 is 48.... and I don't really know how to explain it except tell you that it is Heron's formula and here is a link http://www.mathopenref.com/heronsformula.html but if you understand the rest I think it would be good enough.

Answer 78

Did we ever get the area of the first 12, 12, 12 triangle?

Answer 79

ahhhh im so lost D:

Answer 80

wait okay, so we have 2 triangles. the 10 by 10 by 12 and the 12 by 12 by 12.
the first one's area is 48. we still haven't found the second one.
When we do, what do we do with these in order to find the total area. Add them together?

Answer 81

Well there are a total of 4 triangles, so we need to add 4 things together. Three of the triangles are the same size, but yes you add all four areas together.

Answer 82

right. so 48 stays the same but the other area of the 12 by 12 by 12 would be multiplied by 3?

Answer 83

We did get that the 12 by 12 by 12 triangle has a base of 12 and a height of 6*sqrt(3).

Answer 84

Nooo, =/ it's the other way around, If you look at the picture the three 10's are coming to a point, so the 10's are the ones multiplied by 3

Answer 85

ohhoh ok ok

Answer 86

So the area of the 10 by 10 by 12 is going to be 48
and the area of the 12 by 12 by 12 is going to be 12 * 6 * sqrt(3)

Answer 87

okay. so now what?

Answer 88

Now you have both area's that you need and know that the 10 by 10 by 12 area is multiplied by three and the other area is added to that.

Answer 89

and that is what you need to put into the assignment right?

Answer 90

so 144 + 72 sqrt of 3??

Answer 91

Yup!

Answer 92

NICE! it works! thanks so much! :DD

Answer 93

Your welcome :D!