We have to find the perimeter
and area of the L-shaped polygon.
The perimeter of any polygon,
is the length around the outside of the polygon,
which means to find the perimeter,
we sum the lengths of all the sides.
But notice how we don't have the length
of this side or this side.
Let's work on determining these missing lengths.
Notice how this side has a length of 10.9 meters.
This length must be the same as this missing length
plus this length, which we know is 3.8 meters.
And therefore, to find this missing length,
we subtract 3.8 from 10.9.
10.9 minus 3.8 is equal to 7.1.
This missing length is 7.1 meters.
And next we're going to be determining this missing length.
Notice that this length is 12.6 meters,
which must be the same length as this missing length,
plus the length of this side, which is four meters.
And therefore, the length of this missing side
must be 12.6 meters minus four meters,
which is 8.6 meters.
Now that we have the lengths of all the sides,
we can determine that perimeter.
If we start here, the perimeter is equal to 3.8 meters
plus 12.6 meters, plus 10.9 meters,
plus four meters, plus 7.1 meters, plus 8.6 meters.
Let's write this sum vertically.
Beginning with 3.8, we have 3.8,
plus 12.6.
We need to make sure we do line up
the corresponding place values.
Plus 10.9, plus four,
which I'll write as 4.0,
plus 7.1, plus 8.6.
Before we begin adding, we bring the decimal point down.
Now we begin adding in the tenths place value.
We have eight plus six, which is 14, plus nine,
which is 23, plus one is 24, plus six is 30.
We record a zero in the tenths place value,
perform an exchange,
and write a three in the ones place value.
And now we add the digits in the ones place value.
Three plus three plus two is eight, plus four is 12,
plus seven is 19, plus eight is 27.
Record the seven in the ones place value,
perform an exchange,
and record the two in the tens place value.
In the tens place value, we have two plus one plus one,
which is four.
So now we know the perimeter
equals 47 or 47.0 meters.
Because the units are already given, we enter 47.
And now we need to determine the area.
There's not a special area formula
to determine the area of a L-shaped polygon
and therefore, we will have to decompose this area,
or break it up into smaller areas,
that we can more easily find the area of.
Notice how we could break this up into two rectangles
if we cut the polygon here or here.
Let's go ahead and cut the polygon here.
And now we have two rectangles,
which we can find the area, using the area formula,
length times width.
The area of the given polygon is equal to
the area of this rectangle plus the area of this rectangle.
Notice how the length of the rectangle on the left
is 10.9 meters, this length,
and the width is four meters.
The area of the rectangle on the left
is 10.9 meters times four meters
and then we have plus the area
of the rectangle on the right.
We need to be careful here,
this side has a length of 8.6 meters, not 12.6,
so the length is 8.6 meters and the width is 3.8 meters.
And therefore, the area of the second rectangle
is 8.6 meters times 3.8 meters.
And now we need to determine these two products
and then the sum.
This product must contain one decimal place.
The product is 43.6.
Next we have 8.6 times 3.8.
This product must contain two decimal places.
The product is 32.68.
The area of the L-shaped polygon
is equal to 43.6 square meters
plus 32.68 square meters.
And now we'll find the sum.
We will write 43.6 as 43.60.
The area of the polygon is 76.28 square meters.
Because the units are already given, we enter 76.28.
I hope you found this helpful.