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welcome to math with mr. J in this video
we're going to talk about how to find
the area of a composite figure and on
your screen there we have number one and
number two and those are both examples
of composite figures so what we need to
do in order to find the area of these we
need to separate them into simpler
shapes that we know how to find the area
of that way we can find the area of the
simpler shapes add them together and it
will give us the area of the whole
composite figure so let's jump right
into number one and see exactly what I
mean by that so for number one the first
thing I want to do is again separate
into simpler shapes so I'm going to cut
this into two rectangles I'm going to
draw a dashed line here to represent
where I'm cutting it now I'm going to
name the left rectangle a and the right
rectangle B and it's going to that's
going to help keep me organized as I
work through this problem so I know that
finding the area of a rectangle area
equals length times width so now let's
find the area of a rectangle a and
rectangle B so a and B so area equals
length times width all right now I need
to plug in lengthen width so my length
for a is going to be this eight all the
way up right don't use this six because
this six doesn't go the full length of
the rectangle so you have to be careful
which measurements you use so I'm going
to use the eight and I'm going to
multiply it by the width of three and
that gives me an area of 24 square
inches
so the area of a area equals 24 square
inches now let's do B area equals length
times width let's plug in length is
going to be this 2 inches here so 2
times the width of 7 inches do not use
the 10 the 10 goes all the way across
we only want right here which is that 7
inches so area equals 2 times 7 14
square inches so the area for B is 14
square inches so now that we have the
left rectangle and the right rectangle
the area of those we add those together
in order to get the area of the whole
shape so we would do 24 plus that 14 and
that gives us an answer of 38
so our final area is 38 square inches so
again we separated into simpler shapes
and then found those areas added them
together for the area of the whole
composite figure now for number one we
could have cut that this way as well and
made a top and a bottom rectangle so
usually there's multiple ways to
separate a composite figure it doesn't
matter which way you separate it but it
does matter which numbers you use which
dimensions you use going around for your
length and width so that's something you
need to be careful of so let's jump into
number two here and see how we do this
one this one's a little more complex now
for this one I'm going to cut it in two
or separate it into three simpler shapes
here and I have two rectangles on a
square so I'm going to name
a B and C so let's find the area of
these three so area equals length times
width I'll put my formula first and then
what we will plug in so for a our length
is going to be this five all the way up
so we have five centimeters times the
width of two centimeters and that gives
us an area of 10 square centimeters so
let's do B now B we have a length of
right here or right here and we don't
have a measure there so we're going to
need to figure it out so we know the
whole shape is five centimeters right so
if we have this three what's this going
to have to be in order to get us to that
five centimeters well it's going to have
to be two centimeters and again I
figured that out because this 3 right
here Plus this 2 centimeters equals the
total height of the five centimeters
given to us on the left and right hand
side so sometimes in composite figures
you have to figure out some measurements
that aren't given so our length is going
to be two times the width of three
centimeters which is given so two times
three gives us six square centimeters
and lastly for C we have a square here
five by five square so our length is
five and our width is 5 so our area is
going to be 25 square centimeters so now
we need to add these together 10 plus 6
plus 25 10 plus 6 is 16
+25 is going to give us 41 so the area
I'm going to put it in the top right
corner where I have some room area
equals 41 square centimeters and that's
our final answer
for number two now just like number one
there's multiple ways to solve for that
answer but again what's most important
is picking out the correct measurements
for your lengths and widths thanks so
much for watching until next time peace
