Surface Area of a Triangular Prism Part 1 Math Help Tutorial


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.
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