Hi guys welcome to part 2, you know they say that beauty is only skin deep. Well in this
pyramid it is a beauty but we only after the skin in other words the surface area, the
total, complete exterior covering of this particular pyramid right over here. Now we
are going to take in 4 steps. The first step what we need to do as I mentioned in part
1 is we need to find this slant height across there and that is equivalent to this right
over there yeah. so that is what we are going to find thus it make sense? And then after
that what we got to do? is we are going to actually used that slant height that become
the vertical perpendicular height pace of that triangle we are going to use ½ x base
x height to work out the area of that pace then all we need to do is multiply that by
4 because there are 4 paces of triangle all around and then finally what we need to do
to work out this area under here that is the base that is the square base is going to be
pretty easy 10 by 10 and all we have to do to finalized this is to add up all those sides
five sides to come up with the complete total entire surface covering and skin of this pyramid.
So let us start at part 1 that is to work out this slant height right across there.
we are going to use a guys names by Pythagoras he came up with the Pythagoras theorem or
after the hypotenuse as you can see here. So let us start to fill this in, so the hypotenuse
across here is what we are looking for and that is actually S the slang height across
there because that is the pace right in there we want that front triangle paces flat on
the ground that is what we want so how we do that? Well the slant is what been missing
let us look at the dimension we do have. well we do have 12 the vertical height right there
that is the perpendicular height from the base in the middle of square all the way up
to a peak or the peak and that is 12.Now across here is half way across, so they only way
can find this by observing this diagram displayed here we have this corner to that corner that
is 10cm so if we half that is going to be 5cm because it is a half way between there
yeah. so let us put down 5 here ok there is our
right angle triangle and we can use by Pythagoras theorem so let us do that right now. So it
is going to be, we are looking to the hypotenuse so therefore it is going to be S squared which
is the slant = 12 squared + 5 squared so let us work this out. 12 squared 12 x12 is 144
and 5 squared is a 25. Now that is S squared let us add them together 144+25 together,
all together total is 169, all we need to do to with that 169 is to square root that
because S squared, therefore S the slant length which is right cross there because if we flattened
that out it is going to be the perpendicular height of the triangle. The square root of
169 is 13cm and now let us used that to step no.2. so we can work out the actual area of
that paces. Let us work out the area of that paces because
it is the same as the other all 3 paces we need to drop that little triangle so just
let me draw that—there is our perpendicular height of the pace that is 13 now across the
base is 10 is in it? that is 10 so we use the formula ½ x base x height I am sure that
many of you is aware of that formula that is the area of a triangle and we have the
perpendicular height to do that. Area = ½ x the base is 1o and the height is 13 so let
us work that out ½ x 10 is 5, 5 x 13 is 65 that means the area of this paces is 65cm
squared. now that we have that how many other paces do we have? We have another 3 altogether
there are 4 of them, all we need to do is to multiply that by 4 to get pace, pace, pace,
pace there are 4 triangular paces covering the square pyramid so let us multiply that
by 4 so it is going to be -- 4 x 65 on your calculator is 260 --so that is the collective
triangle 4 of them so that is the triangular part that is 4 of them all we need to do is
add the square base down the bottom right here. Now that is f10cm by 10cm it is a perfect
square 10 x10 is a 100 that is the area of the base of the pyramid that is going to be
100 let me write that down all we need to do now is to add all 5 paces
there are 4 here for the triangle and there is 1 square base add that together and that
is going to give us the entire, complete total surface area skin covering of this square
pyramid let us work that now so it is 260 – 260 +100 add the 100 to 260 is 360 and
the is in cm squared the total surface area of this pyramid square so let me write that
up.
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