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in this video we're gonna focus on

calculating the area of a rhombus so

let's say if the diagonal that is the

distance between points B and C let's

say that diagonal is 15 units long and

the other diagonal between a and C let's

say it's 12 units long what is the area

of this particular promise the area of a

rhombus is 1/2 times the product of the

two diagonals so the first diagonal

let's call it 15 and the second one

let's call it 12 one half of 12 is 6 and

6 times 15 well 6 times 10 is 60 6 times

5 is 30 60 plus 30 is 90 so 6 times 15

is 90 and so that's how you can

calculate the area of a rhombus if

you're given the left of the two

diagonals now let's work on another

problem that's similar but also quite

different so once again let's say if we

have rhombus a b c d and also diagonal

AC and diagonal BD and they intersect at

Point E now the two diagonals they meet

at right angles now let's say if segment

B E is equal to 8 at segment C E is

equal to 10 what is the area of the

rhombus so this is 8 and this is 10 how

can we calculate the area now you need

to know that the diagonals of a rhombus

they're perpendicular bisectors of each

other they're perpendicular in the sense

that they meet our right angles and they

bisect each other so AE and EC are

congruent and B E is congruent to Eadie

so therefore that means that Eadie is 8

and AE is 10

so now we have the left of the to

diagnose so diagonal AC is ten plus ten

or twenty units long and diagonal BD is

eight plus eight or 16 is long so we

could use this formula again it's 1/2 D

1 times D 2 so D 1 is 16 D 2 is 20 half

of 16 is 8 and 8 times 20 if you have 8

$20 bills you have 160 bucks so this is

going to be 160 and so that's another

way in which you can calculate the area

of a rhombus if you're given those two

sides

is another problem for you so given the

same type of rhombus rhombus ABCD and

what's gonna say this is point e let's

say if we're told that CD is 17 units

long and AE is equal to 8 calculate the

area of the rhombus

so AE is 8 and CD is 17 how can we

calculate the area with this given

information you need to know that the

four sides of a rhombus are congruent so

therefore a B is 17 now we can calculate

B e because the rhombus can be broken up

into four couldn't grew a triangles so

let's focus on the right triangle the

hypotenuse is 17 and the base is 8 what

is the height how can we figure this out

so we need to use the Pythagorean

theorem see the hypotenuse is 17 a is 8

and let's calculate B 17 squared that's

289 8 times 8 is 64

now 289 minus 64 is 225 and so that's

equal to B squared and if we take the

square root of both sides the square

root of 225 is 15 so b e is 15 units

long

so now we can calculate the area so if B

E is 15 that means II D is 15 and if a E

is 8 E C is also 8 so this diagonal is

gonna be 8 plus 8 or 16 units long and

this one is 15 plus 15 or 30 units long

so the area is 1/2 d1 times d2 so that's

gonna be 1/2 times 30 times 16 so half

of 30 is 15 and 15 times 16 that's 240

and so that's the area of this

particular rhombus it's 240 square units

and the perimeter of a rhombus is 20 if

the length of one of the diagonals is

six what is the area of the rhombus so

let's draw a picture

so if we're given the perimeter what is

the side length of the rhombus keep in

mind that all four sides are congruent

so this is s then all sides are s so the

perimeter is simply four s so all we

need to do is divide the perimeter by

four and that will give us the side

length of the rhombus 20 divided by 4 is

5 so this is 5 units long now the length

of one of the diagonals is 6 so let's

say AC is 6 that means that a is 3 and

EC is also 3 so now we can calculate the

missing side of the right triangle we

can calculate B e so C squared is equal

to a squared plus B squared C the

hypotenuse is 5 a is 3 so let's

calculate B 5 squared is 25 3 times 3 is

9 and 25 minus 9 is 16 so 16 is equal to

B squared and now let's take the square

root of both sides so the square root of

16 is 4 so we have a 3 4 5 right

triangle so now we can calculate the

area so if B e is for e D is 4 which

means that diagonal BD is 8 so the area

is gonna be 1/2 D 1 times D 2 so that's

gonna be 1/2 times 8 times 6 now half of

a is 4 and 4 times 6 that's 24 and so

that's the area of this particular

rhombus it's 24 square units

now let's say this side is 30 and let's

say this part is 15 what's the area of

this rhombus so what do you think we

need to do now you need to know that a

rhombus is a type of parallelogram and

so a square is a parallelogram as well a

rectangle is a parallelogram and the

area of any type of parallelogram is the

base times the height in the case of a

rectangle the area is left times the

width but you can also treat this as

base times height you get the same thing

for a square the area is s squared or s

times F which is also based on site so

for any parallelogram whether it be it a

rectangle or square or rhombus the area

is based on site so the base of this

particular rhombus or parallelogram is

30 now we can see that the height is 15

so the area is just 30 times 15 and so

it's 450 square units

try this problem so let's say if we have

R on this ABCD and let's say that BC is

let me think about this let's say BC is

25 and BD is 24 actually let's make BD

14 so if BC is 25 and BD is 14 what is

the area of the rhombus

how can you calculate the area of this

figure well first what we need to do is

draw the other diagonal so we can't just

multiply base times side we don't know

the length of the height in this

particular case so we can't treat this

like a typical parallelogram

now if BC is 25 and if BD is 14 that

means B II has b7 and Edie has b7 as

well so now we just got to find a

missing side of this right triangle so

the hypotenuse is 25 the height of that

triangle 7 let's calculate the base of

the triangle so C squared is a squared

plus B squared C squared is 25 a is 7

and B is what we're trying to find that

25 times 25 is 625 7 times 7 is 49 and

so 625 minus 49 that's 576 so now let's

take the square root of both sides the

square root of 576 is 24 so C e is 24

and AE is also 24

so we can say that D 1 which is AC

that's 24 plus 24 or 48 and D 2 which is

BD that's 7 plus 7 or 14 so a is equal

to 1/2 D 1 times D 2 so that's 1/2 of 48

times 14 so 1/2 a 48 is 24 so now we

just gotta multiply 24 by 14 and so the

area of this particular rhombus is 336

square units so now you know how to

calculate the area of a rhombus