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 6×7 is 42 so right side of the phase, area of the right equals 6×7
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 14×7 so area
for b, b for bottom=14×7 and that yields a total of 14×7 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 14×7
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
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Surface Area of a Trapezoid – VividMath.com
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