Here’s a new parallelogram lawn you’ve been asked to mow. What
should you charge for mowing it?
Parallelogram area = 45 x 16
= 720 meters
Mowing charge = $0.10 x 720
What if I only have one pair
of opposite sides? Do I still have a
A:No. In order for a shape to be a
parallelogram, both pairs of opposite sides
must be parallel. If you only have one pair
of opposite parallel sides, your shape isn’t a
Can I still use the same formula
for finding the area for that shape?
A:This formula is specific to
parallelograms. But keep reading,
we’re going to cover more than just
parallelograms and we might have just the
formula you need.
What if I only know the length of
the sides of a parallelogram and not the
height? Can I still work out the area?
A:You can’t, because you need to know
what the height is. The reason for this is
that the degree to which the parallelogram
“slants” can make a big difference to the
overall area. As an example, if the sides
of a parallelogram are tilted so that they’re
almost horizontal, you’ll have a much
smaller area than if the sides are almost
But what if I have extra
information such as the internal angles
of the parallelogram? Can I work out the
A:Yes, it is possible to find out the area,
but it takes a bit more work, not to mention
Are opposite sides always the
A:Yes they are, because opposite sides
of a parallelogram are always congruent
(same angle, same length). If opposite
sides are different lengths, you don’t have a
What about opposite angles? They
look the same to me.
A:Yes, for parallelograms opposite
angles are always congruent. Similarly,
consecutive angles are supplementary. You
can use the angle skills you developed
earlier in the book to work this out.
246 Chapter 6