SURFACE AREA OF PRISM-TRAPEZIUM
HI guys I am going to show to you a phenomenal and fantastic way to find the phases of this
trapezium prism, what I am talking the surface area, another words the space all over each
individual exterior phase that is why we are going to work out. Now this trapezium prism
that is going to has 6 phase and we are going to do it in five simple and straight forward
steps. And now in order to work this out first of all we are going a need to find the front
phase first why? Because that is the trapezium part is, see that trapezium parallel lines
and two lines coming from out there we do have vertical height perpendicular right there.
So let us go to step no. 1, now before we do that, all unit are all in meter, so the
answer is going to be in meter squared so let us find out the full scope of the entire
space all over the skin of this trapezium prism. Step no. 1, as I said earlier is to
work out the phase this front one here is a trapezium, let us work that out. So the
formula for the area of a trapezium is, if you do not recall it, you may want to revise
it from the other chapter but feel free to watch now as I go through it to lots of detail
for you. So I got a ½ x the height, the height has to be perpendicular height , there is
that perpendicular height there happens to be 5m. and the a + b are the two parallel
lines top and bottom we got 10m across here so that 10, that is also 10 there yeah can
you see that? That is 1o equal because that is 10 and the bottom here, the base we have
14m so that is going to have a and b respectively so, let us plug in drag in drop those numbers
into formula we can work out the trapezium area of the front phase, by the way if the
front phase comes to a certain amount the back phase would be exactly the same. So let
us work that out, vertical height 5 a across here is 10, and b the base is 14. Ok let us
point in our calculators, so it is going to be a ½ x 5 times which is 2.5 times 10 +
14, 10 + 14 is 24, so multiplying all that three out the area of the front phase all
together in your calculator and is going to yield 60m squared, ok that is the front phase
which means that back phase is going to be also 60m square let us put area back. Ok this
is the area of the back we got the front and the back and now where we goes to the right
side of the phase, and the right side of the phase is right over there you can see the
slant length over there is 6 and the dept is 7 all we need to do now length times breth
and we will that out simple area of that breath rectangle right there 6x7 is 42 so right side
of the phase, area of the right equals 6x7 which equal 42m squared so there is the right
side, now the right side is 42, the left side guess what? The left side because it is symmetrical
is exactly the same it is that also going to be 42, so area left is equal to 42m squared,
so we got the front we got the back, we got the right, we got the left. Now let us work
the area right at the top up there, what is that area? So what is going to be 10 across
there time the depth there is going to be 10 times the dept is written like this, 7
there, that is also 7 there so 1o x 7, that is going to give us 70 so that is top phase
there, area of top, now if the area of the top is 70m squared, is the area of the bottom?
Is no, let us have a look here, the bottom is 14 across there and the depth is 7 across
there so that is going to be 14x7 so area for b, b for bottom = 14x7 and that yields
a total of 14x7 that is 98m squared and now we have work out 6 phases, let us check if
we got 6, one, two, three, four, five, and six therefore we have all 6 phases all we
have to do now is add them all together to get the complete space surface space of this
trapezium prism, so let us add them all together. So, we have the two 60’s which are the areas
of the front phase and the back phase, write that up, and then we have the two 42’s which
are the right and the left phase and then we have finally the top which is up there
which is 70 and the bottom under there 14x7 which is 98, ok, let us get our calculators
out so we can work out the total, complete and scope and size of skin and the exterior
outside surface of this trapezium prism. In our calculator 60+60+42+42+70+98 grand total,
altogether the entire total complete surface area is 372m squared.
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.