Video Transcript
Determine the area of the given
figure.
Looking at the diagram, we can see
that we have a composite polygon. So, we just need to carefully
identify the individual polygons it’s made up of. Firstly, we have a trapezoid. We know that the two lines which
appear to be horizontal are parallel because they each form a right angle with the
dotted line which appears to be vertical. We then have two congruent shapes,
which are in fact parallelograms. Although, they could each be
divided into a right-angled triangle and another trapezoid.
We know the formulae for
calculating the areas of each of these polygons. Let’s consider the trapezoid first
of all. The two parallel sides 𝑎 and 𝑏
are 16 plus 16 meters, that’s 32 meters, and 46 meters. And the perpendicular height is 14
meters. So, substituting into the formula
for the area of a trapezoid gives 546.
For each of the parallelograms, and
it may help here to turn your head to the side slightly, we see that they have a
base of 27 meters and a perpendicular height of 14 meters. We need to be careful here. It is the perpendicular height we
need, which is 14 meters, not the slant height, which is 16 meters. Remember these two parallelograms
are identical or congruent. So, we can find each area, 27
multiplied by 14, and then double it to give the total contribution, which is
756.
The total area then is 546 for the
area of the trapezoid plus 756 for the area of the two parallelograms, which is
1302. And the units for this area will be
square meters.
Don’t worry if it sometimes takes
you a little bit of time to identify the individual polygons that make up a
composite polygon. It’s worth spending the time to do
this and find the most efficient approach. You may find it helpful to tilt the
diagram and look at it in different orientations.
