We're asked to determine
the perimeter and the area of the rectangle,
where looking at the rectangle notice how
the length is 16.2 meters and the width is 9.4 meters.
Beginning with the perimeter,
remember the perimeter of a polygon
is the distance around the polygon,
which means we can always find the perimeter
by adding the lengths of all of the sides.
Or because we have a rectangle,
we can also determine the perimeter
by using the formula P equals two l plus two w,
where two l is two times the length
and two w is two times the width.
But since the length and width are in decimal form,
I think it'll be easier to add the lengths of the four sides
rather than determine two products
involving decimals and then a sum.
So let's label the lengths of the opposite sides.
We know this length has a length of 16.2 meters.
We know this side has a length of 9.4 meters.
So now if we think about walking around the rectangle,
the perimeter is 16.2 meters, plus 9.4 meters,
plus 16.2 meters, plus 9.4 meters.
So again, the perimeter P is equal to 16.2,
plus 9.4, plus 16.2, plus 9.4.
To determine the sum, though,
it'll be easier to write this sum vertically,
lining up the corresponding place values.
We have 16.2, plus 9.4, plus 16.2, plus 9.4.
Bring the decimal down into the sum,
and now we add, starting with the rightmost place value.
We have two plus four, which is six,
plus two, which is eight, plus four, which is 12.
Record the two.
Perform an exchange with the one.
Adding the ones place value, one plus six is seven,
plus nine is 16, plus six is 22, plus nine is 31.
Record the one.
Perform an exchange with the three.
Adding the tens place value,
three plus one plus one is five.
So we now know the perimeter is 51.2 meters.
Let's go and record this.
Now if we did want to use the formula,
we would have the perimeter P
is equal to two times the length of 16.2 meters,
plus two times the width of 9.4 meters.
Let's check this on the calculator
to make sure we do get 51.2.
And notice how we do, which does verify
the perimeter is correct.
And now let's determine the area.
The area is equal to the number of square meters
that will fit inside the rectangle.
Because we have a rectangle, the area is equal to
l times w, or length times width.
Which means the area
is equal to 16.2 meters, times 9.4 meters,
which will give us the units of meters squared.
Let's go ahead and find this product by hand.
We have 16.2 times 9.4.
Notice both factors contain one decimal place,
and therefore the product will contain two decimal places.
We begin by multiplying by the four.
Four times two is eight.
Four times six is 24, record the four,
perform an exchange with the two.
Four times one is four, plus two is six.
Before multiplying by the nine,
we place a zero below the eight, and now we multiply.
Nine times two is 18, record the eight,
perform an exchange with the one.
Nine times six is 54, plus one is 55.
Record the five, perform an exchange with the other five.
Nine times one is nine, plus five is 14.
And now we add, eight, four plus eight is 12,
record the two, perform an exchange.
One plus six plus five is 12,
record the two, perform an exchange.
One plus four is five, and we have a one.
But again, the product must contain two decimal places,
and therefore the product is 152.28,
and therefore the area is 152.28 square meters.
So this is the area, but we'll go ahead
and check it on the calculator before we go.
16.2
times 9.4
is 152.28, verifying the area is correct.
I hope you found this helpful.