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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