Video Transcript
The area of a trapezoid is capital
𝐴 is equal to one-half ℎ multiplied by 𝑎 plus 𝑏. Find capital 𝐴 when ℎ is equal to
six centimeters, 𝑎 is equal to 10.5 centimeters, and 𝑏 is equal 16.8
centimeters. Give your answer approximated to
one decimal place.
In this question, we are given a
formula for the area, capital 𝐴, of a trapezoid in terms of three values: ℎ, 𝑎,
and 𝑏. We need to use given values for
these three variables to determine the area of the trapezoid to one decimal place of
accuracy.
Before we start answering this
question, we can add the given information onto the diagram. We can start by recalling that a
trapezoid is a quadrilateral with one pair of parallel sides. In this case, it’s the sides with
lengths labeled 𝑎 and 𝑏. Next, we can note that the values
of 𝑎 and 𝑏 are the lengths of the parallel sides. So we have that 𝑎 is equal to 10.5
centimeters and 𝑏 is equal to 16.8 centimeters. Finally, ℎ is the perpendicular
distance between the parallel sides of the trapezoid. This is often referred to as the
height of the trapezoid. We are told that this is six
centimeters.
To find the area of the trapezoid,
we need to substitute these values into the given formula and evaluate. Substituting ℎ is equal to six, 𝑎
is equal to 10.5, and 𝑏 is equal to 16.8 into the formula gives us that the area of
the trapezoid is equal to one-half times six multiplied by 10.5 plus 16.8.
In the order of operations, we
start with the operations inside the parentheses. So we need to start by adding 𝑎
and 𝑏 together. We could do this by converting them
into fractions. However, we can directly calculate
that 10.5 plus 16.8 is equal to 27.3. Therefore, the area of the
trapezoid is given by one-half times six times 27.3.
We now have a product of three
rational numbers. So we can evaluate the product in
any order that we want. We can see that one-half times six
is three. So we have three times 27.3. We now need to evaluate this
product. We can do this by multiplying the
integer part and decimal parts by three, separately. We calculate that three times 27 is
equal to 81 and three times 0.3 is 0.9. So we add these to see that the
product evaluates to give us 81.9.
Finally, since this is an area and
the lengths are measured in centimeters, we can give this area the units of square
centimeters. It is worth noting that we did not
need to round at any point in our calculations. So the answer is exact.
Hence, the area of a trapezoid with
height six centimeters and parallel sides of lengths 10.5 centimeters and 16.8
centimeters is 81.9 square centimeters.
