area of the lovely el “area” means the space taken up by this shape… … so really, we should...

Area of the Lovely El

“Area” means the space taken up by this shape…… so really, we should imagine it ‘filled in.’(You could shade it in with your pencil too )


How many square spaces does it taketo fill up this shape?


This one has twenty.Yup! We could just count them.

Let’s try to think of area as something real, taking up space

Let’s make the formula make sense!

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One of the best ways to figure out something complicated

is to break it into simpler pieces, figure them out, *and then* finish the job by putting the pieces together.

(This is not to be confused with “well, this is too hard, soI’ll do something simpler and hope it’s good enough.”

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Area

• “I DON’T KNOW HOW TO FIGURE OUT THE AREA OF A WEIRD SHAPED BLOCK!”

• … okay, what *do* you know how to figure out?

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Area

• We can break this up into rectangles.

• The big rectangle has two squares of space in the first row…

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2cm

Area

• there are 8 rows of two squares each… here’s another place where “of” is showing multiplication

•

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2cm

8cm

Area

• there are 8 rows of two squares each… here’s another place where “of” is showing multiplication

• This rectangle’s area is 16cm2

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2cm

8cm

Area

• Think “area: square ya!”

• Since we’re measuring squares – two dimensions – our unit is raised to the second power.

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2cm

8cm

Area

• What about the other guy?

• It’s 4 x 1 or 4cm2

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2cm

8cm

1cm

4cm

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Area

• So, together… this shape has 20 cm2

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2cm

8cm

1cm

4cm

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Area

• So, together… this shape has 20 cm2

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2cm

8cm

Breaking into rectangles

But how can you tell where to break it up?

7cm

4cm

1cm

6cm

8cm

2cm


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8 7

We can break this “el” into two rectangles.

This one… but what numbers are its length and width?

Breaking into rectangles • It’s the 8 and the 2

• Trace the rectangle … • The six goes further than

the base of the rectangle…

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8 7

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Should stop here!!!

Breaking into rectangles • It’s the 8 and the 2

• The six goes further than the base of the rectangle…

• And the 7 doesn’t go to the end.

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8 7

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15 16

Should end here!


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8 7

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15 16

This rectangle is left… And the six is too big here, too!

It’s 1 x 4, or 4.

So our area is 16 + 4, which is 20…

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8 7

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Or, we could have split it this way:

7 x 2 (the 8 is too long!)

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8 7

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Or, we could have split it this way:

7 x 2 + 6 x 1 = 14 + 6 =

20 -- different ways to get the same answer.

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Back to this harder one – no, it’s not the same!(Centimeters are really bigger than this; this is a picture of it, so it’s smaller.)

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6 cm

20 cm

5 cm

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14 cm


Break it up and find the right sides to multiply.

You don’t have to solve it – just set it up!

Don’t click ‘til you’ve made your equation

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14 cm




It should be 20 x 6 + 20 x 5 = 120 + 100 = 220 cm

OR>>>>

25 cm

6 cm

20 cm

5 cm

20 cm

14 cm




It could also be 25 x 6 + 5 x 14

150 + 70 = 220

25 cm

6 cm

20 cm

5 cm

20 cm

14 cm

area of the lovely el “area” means the space taken up by this shape… … so really, we should...

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