Video Transcript
The given figure shows a
backyard. Determine its area in square
centimeters. If the backyard was priced for four
dollars per square meter, determine how much the backyard would cost.
So let’s consider the diagram of
the backyard we are given, which is a quadrilateral. On the diagram, there are two
angles with a measure of 90 degrees, so this dashed line which represents one of the
lengths of the backyard is at 90 degrees to the other length. Now because these angle measures
are both the same, at 90 degrees, that gives us a clue about the relationship
between the top and lower bases in this diagram.
We can recall that if we have two
lines which are perpendicular to the same line, then the two lines must be
parallel. This is really an extension of the
fact that if we have a transversal of two lines where corresponding angles are
equal, then the lines are parallel. The reason why this is important
here is that because these two lines in the diagram are parallel, then we can say
something about the specific quadrilateral that this is. It must be a trapezoid, as a
trapezoid is defined as a quadrilateral with one pair of parallel sides. And this will allow us to calculate
the area of this backyard.
To find the area of a trapezoid, we
calculate one-half times 𝑎 plus 𝑏 times ℎ, where 𝑎 and 𝑏 are the lengths of the
parallel bases and ℎ is the perpendicular height. We can take the lengths of 𝑎 and
𝑏 as 56 and 30 meters, respectively, although it doesn’t matter which of the two
values we designate with 𝑎 and 𝑏. The perpendicular height is 21
meters. So when we input these values into
the formula, we have that the area equals one-half times 56 plus 30 times 21. We can simplify the parentheses to
86 and then find half of this. And 43 times 21 is 903.
Now the units for this will be
square meters, since each of the measurements were given in meters. But notice that we need to give the
area in terms of square centimeters.
Now we might recall that one square
meter is 10,000 square centimeters. But if we forget, there is a quick
way to work this out. Let’s imagine we have a square that
is one meter by one meter. To find its area, we multiply one
meter by one meter, which is one square meter. Then if we take the same square and
this time measure it in centimeters, it would be 100 centimeters by 100
centimeters. Therefore, its area can be
calculated in square centimeters as 10,000 square centimeters, which is where this
conversion fact that one square meter is equal to 10,000 square centimeters comes
from. So, we need to convert the area of
903 square meters to square centimeters. And therefore, we multiply 903 by
10,000, which gives 9,030,000 square centimeters. And that’s the first part of the
question answered.
Next, we need to calculate the cost
of the backyard given that it is four dollars per square meter. So, we can use the area of the
backyard, that’s the trapezoid, that we calculated in square meters. If it costs four dollars per square
meter, then we must multiply the 903 square meters by four, which is 3,612
dollars. We can give this answer as whole
dollars or including the zero cents; it doesn’t really matter. So, the area in square centimeters
is 9,030,000 square centimeters, and the total cost is 3,612 dollars and zero
cents.
