Find the height of the trapezoid shown below
if the area equals 378.56 square units.
The area formula for a trapezoid
is area equals one half times
the quantity B sub one plus B sub two times H
where B sub one and B sub two
are the lengths of the two bases.
In a trapezoid the bases are the two parallel sides.
So we'll call this base one
and we'll call this base two.
Let's go ahead and label this B sub one
and this B sub two.
The height would be this length here.
So we'll label this H.
Because we know the area we can now setup
an equation using the area formula
to determine the height.
The area is equal to one half
times the quantity B sub one plus B sub two,
which should be the quantity 26 plus 10.4,
times the unknown height
and this must equal a given area of 378.56 square units.
Now we need to solve the equation for H.
Let's first simplify the left side of the equation.
Simplifying inside the parenthesis.
26 plus 10.4 equals 36.4,
so we have one half times 36.4
times H equals 378.56
and one half times 36.4
is equal to half of 36.4
which equals 18.2 or we can write 36.4 as a fraction
with the denominator of one.
This will give us 36.4 divided
by two times H equals 378.56.
36.4 divided by two is equal to 18.2
so we have 18.2h equals 378.56.
Of course if we need too we can show this quotient
36.4 divided by two.
Move the decimal point up into the quotient
and divide like we normally do.
Notice how the divisor is already a whole number.
So there's one two in three,
one times two is two.
Subtract, bring down the six.
There are eight two's in 16.
Eight times two is 16.
Subtract, bring down the four.
There are two two's in four.
Two times two is four.
Subtracting the difference is zero.
Verifying the quotient is 18.2.
Of course we can verify this on the calculator as well.
36.4 divided by two is 18.2.
Because 18.2h means 18.2 times H,
to solve for H we need to undo this multiplication
by dividing both sides by 18.2.
Dividing by 18.2 undoes multiplying by 18.2
and therefore the left side simplifies to H
or 18.2 divided by 18.2 is one,
one times H is H and therefore H is equal to this quotient.
Let's first show it by hand.
So we have 378.56
divided by 18.2.
Notice here the divisor is not a whole number
therefore the first step is
to move the decimal point to the right one place
so the divisor is a whole number.
We can do this as long as we do the same to the dividend,
so we'll move the decimal point
to the right one place here as well.
Then up into the quotient.
Then divide like we normally do.
The first step is to determine how many 182's are in 378,
which is two.
Multiplying two times two is four,
two times eight is 16, perform an exchange,
two times one is two, plus one is three.
Subtracting.
Eight minus four is four.
Seven minus six is one.
Bring down the next digit which is five.
Notice how this is less than 182
so there are zero 182's in 145.
Zero times 182 is zero.
Subtracting the difference is 145.
Bring down the last digit.
We now need to determine how many 182's
are in 1456.
I believe that's eight.
Multiplying eight times two is 16.
Perform an exchange.
Eight times eight is 64 plus one is 65.
Perform an exchange with the six.
Eight times one is eight plus six is 14.
Notice how the difference is zero.
Therefore the quotient is 20.8.
Therefore H equals 20.8
which means the height of the trapezoid
equals 20.8 units.
Let's also verify this quotient on a calculator.
We have 378.56
divided by 18.2
which is 20.8.
I hope you found this helpful.