Head First 2D Geometry

Look f

amiliar? It’s the

same f

ormula y

ou’d use

t

o ca

lcula

te the ar

ea

of a r

ec

tangle.

T

he dotted line s

hows

W

e mov

ed the end triangle

t

o f

orm a r

ec

tangle.

quadrilaterals

If you don’t like what you’re given, change it

True, geometry has lots of rules, but moving things around doesn’t mean you’re

breaking them. By moving the shapes you created in the parallelogram around,

you were able to form a rectangle. And you know that it has the same height and

same base width as the original parallelogram. So now…you know how to find

the area of a parallelogram!

Width

the s

hap

e of the

original para

llelogram.

Height

Parallelogram Area = Base Width × Height

Here’s a new parallelogram lawn you’ve been asked to mow. What

should you charge for mowing it?

45 meters

16 meters

34 meters

you are here 4 245

sharpen solution

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

2

Mowing charge = $0.10 x 720

= $72.00

45 meters

16 meters

34 meters

Q:

What if I only have one pair

of opposite sides? Do I still have a

parallelogram?

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

parallelogram.

Q:

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.

Q:

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

vertical.

Q:

But what if I have extra

information such as the internal angles

of the parallelogram? Can I work out the

area then?

A:Yes, it is possible to find out the area,

but it takes a bit more work, not to mention

some trigonometry!

Q:

Are opposite sides always the

same length?

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

parallelogram.

Q:

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