Uploaded by vividmaths on 19.04.2012

Transcript:

Hi guys, they say that they are 2 side of every story well in this story it is called

Triangular Prism, we are looking of the total surface area of the 5 sides to this story.

Now are looking for the total entire surface area as I said earlier of this particular

triangular prism across here. Now here it is in 3D and we are looking for that and if

we have a bulldozer and we flatten that out and we open that up we get something like

this that we notice it is 5 sides, we have the 2 triangles: the front face and the back

face and then the 3 panels that envelope and wrap around it. so let’s go back in the

original drawing here in 3D across here, now we are going to do this in 2 parts, this is

part 1, in part 1 we are going to get the area of the front face of this triangular

prism and the back face of this triangular prism so this 2 face that we are going to

work out and then in part 2 we are going to come back to work out the entire total complete

area, surface area of this triangular prism but first let’s go back to part 1 and work

out the area of this front and back face of this face now in order to do this is a little

bit of a trick and a twist, we have to work out what the vertical height is right there,

and we are not given a vertical height, we are given only a side, all slant heights so

remember, in order to work out the area of a triangular we need to have the vertical

height, remember the formula? Area of the triangle is half times base times vertical

height, we don’t have the vertical height here, so let’s work that out, let’s get

the vertical height, that’s part 1 – step 1 and then step 2 we are going to work out

the area. So let’s do that, let’s work out the height first the we need to have that

particular theorem to work that out, but first let me just draw a little picture of what

it’s going to look like. So here’s our triangle, and we have 2 sides on each part

of the slant heights and they both exactly the same and they both 7 centimeters – 7

there and 7 there, now the base across the bottom as you can see there is an 8, ok that’s

our front face which is the same as the back face of this triangular prism. Now as you

can see there is 2 lines there and 2 red lines in there indicating that it is an isosceles

– meaning the 2 slant heights are the same so there’s a triangle, what do we need to

do is to chop into half so we can get this vertical height right there, that is what

we after that height. Now what we need to use what theorem to do that, let me just draw

again – we are given, I don’t know the height, we’ve got that the slant height

it’s 7 across the base is 8 and we chop it in half and half of 8 is 4, so that would

be 4 centimeters across the base of the right angle triangle, yes it is a right a angle

triangle and now we can actually work out the height which theorem by theocracies theorem

and I’m going to do briefly and quickly here so we can actually work height that out

so if sure by theocracies theorem go back this chapter revised it then come back and

you do this more confidence so we work this out now , so the height squared equals the

hypotenuse squared minus the bottom length squared that is going to be seven squared

mines four squared this are hypotenuse and this are base therefore there is the four

there hypotenuse lets subtract them so the height square is seven square is forty nine

take away four squared is sixteen that means, four square, forty nine squared minus sixteen

equals thirty three so the height squared is thirty three let us square root of that

right there is what we are after that area and that height is the square root of thirty

three is five point seventy four two, two decimal places, five point for centimeters

let me just write her again that is our vertical height we can now look at quite confidently

the total area of that front face. So the area triangle is half the base times height,

let me write that up, that is our formula let us just substitute the value. Now we have

that height which is good news, the base we have it, because the cross that is eight so

we can work on that front face area and the base is eight times the height we work that

out five point seventy four, let us put that in our calculator, one half times eight times

five point seventy four for the front face that brand are right there gives us a total

of, that concludes part one, stay tuned for part we are going to complete the total entire

surface area of this triangle prism so stay tuned we will be right back.

Take a minute to check out our website at http://www.vividmaths.com. You will find additional

resources, cheat sheets, transcripts and other math videos that are not available on Youtube.

Lastly, don’t forget to subscribe to get access to all the ready answer for all your

math questions plus other special offers.

Triangular Prism, we are looking of the total surface area of the 5 sides to this story.

Now are looking for the total entire surface area as I said earlier of this particular

triangular prism across here. Now here it is in 3D and we are looking for that and if

we have a bulldozer and we flatten that out and we open that up we get something like

this that we notice it is 5 sides, we have the 2 triangles: the front face and the back

face and then the 3 panels that envelope and wrap around it. so let’s go back in the

original drawing here in 3D across here, now we are going to do this in 2 parts, this is

part 1, in part 1 we are going to get the area of the front face of this triangular

prism and the back face of this triangular prism so this 2 face that we are going to

work out and then in part 2 we are going to come back to work out the entire total complete

area, surface area of this triangular prism but first let’s go back to part 1 and work

out the area of this front and back face of this face now in order to do this is a little

bit of a trick and a twist, we have to work out what the vertical height is right there,

and we are not given a vertical height, we are given only a side, all slant heights so

remember, in order to work out the area of a triangular we need to have the vertical

height, remember the formula? Area of the triangle is half times base times vertical

height, we don’t have the vertical height here, so let’s work that out, let’s get

the vertical height, that’s part 1 – step 1 and then step 2 we are going to work out

the area. So let’s do that, let’s work out the height first the we need to have that

particular theorem to work that out, but first let me just draw a little picture of what

it’s going to look like. So here’s our triangle, and we have 2 sides on each part

of the slant heights and they both exactly the same and they both 7 centimeters – 7

there and 7 there, now the base across the bottom as you can see there is an 8, ok that’s

our front face which is the same as the back face of this triangular prism. Now as you

can see there is 2 lines there and 2 red lines in there indicating that it is an isosceles

– meaning the 2 slant heights are the same so there’s a triangle, what do we need to

do is to chop into half so we can get this vertical height right there, that is what

we after that height. Now what we need to use what theorem to do that, let me just draw

again – we are given, I don’t know the height, we’ve got that the slant height

it’s 7 across the base is 8 and we chop it in half and half of 8 is 4, so that would

be 4 centimeters across the base of the right angle triangle, yes it is a right a angle

triangle and now we can actually work out the height which theorem by theocracies theorem

and I’m going to do briefly and quickly here so we can actually work height that out

so if sure by theocracies theorem go back this chapter revised it then come back and

you do this more confidence so we work this out now , so the height squared equals the

hypotenuse squared minus the bottom length squared that is going to be seven squared

mines four squared this are hypotenuse and this are base therefore there is the four

there hypotenuse lets subtract them so the height square is seven square is forty nine

take away four squared is sixteen that means, four square, forty nine squared minus sixteen

equals thirty three so the height squared is thirty three let us square root of that

right there is what we are after that area and that height is the square root of thirty

three is five point seventy four two, two decimal places, five point for centimeters

let me just write her again that is our vertical height we can now look at quite confidently

the total area of that front face. So the area triangle is half the base times height,

let me write that up, that is our formula let us just substitute the value. Now we have

that height which is good news, the base we have it, because the cross that is eight so

we can work on that front face area and the base is eight times the height we work that

out five point seventy four, let us put that in our calculator, one half times eight times

five point seventy four for the front face that brand are right there gives us a total

of, that concludes part one, stay tuned for part we are going to complete the total entire

surface area of this triangle prism so stay tuned we will be right back.

Take a minute to check out our website at http://www.vividmaths.com. You will find additional

resources, cheat sheets, transcripts and other math videos that are not available on Youtube.

Lastly, don’t forget to subscribe to get access to all the ready answer for all your

math questions plus other special offers.