We're asked to determine the perimeter
and area of the given trapezoid.
The perimeter is a distance
around the outside of the trapezoid,
so if we think of walking around the trapezoid
starting here, the perimeter is equal to 11.3 feet
plus 10.5 feet
plus 11.3 feet
plus 16.8 feet.
So again the perimeter, P
is equal to 11.3 feet
plus 10.5 feet
plus 11.3 feet
plus 16.8 feet,
because we have decimals, let's determine this vertically,
lining up the corresponding place values.
Now I bring the decimal point down into the sum
and add the rightmost place value,
we have three plus five, which is eight
plus three, which is 11,
11 plus eight is 19,
record the nine, perform an exchange with the one,
adding the one's place value, we have one plus one
plus one plus six, which is nine,
adding the 10's place value, we have one plus one
plus one plus one, which is four.
So the perimeter, P
is equal to 49.9 feet.
Before we determine the area,
let's check the sum on the calculator.
We have 11.3
plus 10.5
plus 11.3
plus 16.8,
enter, which does verify our result
and now let's work on determining the area of the trapezoid.
The area of a trapezoid is equal to one half
times the sum of the two bases times the height,
where the bases are the two parallel sides,
so one base has a length of 16.8 feet,
the other base has a length of 10.5 feet,
let's call the bottom base B sub one
and the top base B sub two
and the height is 6.3 feet,
which means the area of the trapezoid is equal
to one half times the sum of the two bases,
which is 16.8 feet plus 10.5 feet,
times the height of 6.3 feet
and now let's begin simplifying.
Let's first simplify inside the parentheses
by determining this sum,
we have 16.8
plus 10.5,
eight plus five is 13, perform an exchange with the one,
one plus six is seven and one plus one is two,
this sum is 27.3 and because we have decimals here,
let's also write one half as a decimal,
one half is equal to five-tenths or 0.5,
so we know the area is equal to 0.5 times the sum,
which is 27.3
times 6.3
and now let's multiply from left to right.
For 0.5 times 27.3,
let's determine the product in the reverse order
as 27.3
times 0.5,
because both factors contain one decimal place,
the product must contain two decimal places
and now multiplying five times three is 15,
record the five, perform an exchange,
five times seven is 35 plus one is 36,
record the six, perform an exchange
and five times two is 10 plus three is 13.
Again the product must contain two decimal places
and therefore the product is 13.65,
so we now have the area is equal to 13.65
times 6.3.
Let's determine this last product
to determine the area of the trapezoid.
Notice now the first factor has two decimal places,
the second factor has one decimal place
and therefore the product must contain three decimal places.
We begin by multiplying by the three,
three times five is 15,
record the five, perform an exchange,
three times six is 18 plus one is 19,
record the nine, perform an exchange,
three times three is nine plus one is 10,
record the zero, perform an exchange
and three times one plus one is four
and now before multiplying by six,
we place a zero below the five in the rightmost place value
and now I multiply by six,
six times five is 30, record the zero, perform an exchange,
six times six is 36 plus three is 39,
record the nine, perform an exchange,
six times three is 18 plus three is 21,
record the one, perform an exchange
and six times one is six plus two is eight
and now we add
and again the product must contain three decimal places
and therefore the product is 85.995,
which means the area is 85.995,
because the lengths are in feet,
the area is in square feet or feet squared.
Before we go, let's check our work on the calculator.
Let's go ahead and enter the area in this form here,
where we have one half or one divided by two
and then in parentheses, 16.8
plus 10.5
and then times 6.3,
enter and notice how this does verify our work is correct.
I hope you found this helpful.