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Area Formulas. Rectangle. Rectangle. What is the area formula?. Rectangle. bh. What is the area formula?. Rectangle. bh. What is the area formula?. What other shape has 4 right angles?. Rectangle. bh. What is the area formula?. Square!. What other shape has 4 right angles?.

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Presentation Transcript
rectangle1

Rectangle

What is the area formula?

rectangle2

Rectangle

bh

What is the area formula?

rectangle3

Rectangle

bh

What is the area formula?

What other shape has 4 right angles?

rectangle4

Rectangle

bh

What is the area formula?

Square!

What other shape has 4 right angles?

rectangle5

Rectangle

bh

What is the area formula?

Square!

What other shape has 4 right angles?

Can we use the same

area formula?

rectangle6

Rectangle

bh

What is the area formula?

Square!

What other shape has 4 right angles?

Can we use the same

area formula?

Yes

practice

Practice!

17m

Rectangle

10m

Square

14cm

answers

Answers

17m

Rectangle

10m

170 m2

Square

196 cm2

14cm

triangle

Triangle

So then what happens if we cut a rectangle in half?

What shape is made?

triangle1

Triangle

2 Triangles

So then what happens if we cut a rectangle in half?

What shape is made?

triangle2

Triangle

2 Triangles

So then what happens if we cut a rectangle in half?

What shape is made?

So then what happens to the formula?

triangle3

Triangle

2 Triangles

So then what happens if we cut a rectangle in half?

What shape is made?

So then what happens to the formula?

triangle4

Triangle

2 Triangles

So then what happens if we cut a rectangle in half?

What shape is made?

bh

So then what happens to the formula?

triangle5

Triangle

2 Triangles

So then what happens if we cut a rectangle in half?

What shape is made?

bh

2

So then what happens to the formula?

practice1

Practice!

Triangle

14 ft

5 ft

answers1

Answers

Triangle

14 ft

35 ft2

5 ft

parallelogram

Parallelogram

Let’s look at a parallelogram.

parallelogram1

Parallelogram

What happens if we slice off the slanted parts on the ends?

Let’s look at a parallelogram.

parallelogram2

Parallelogram

What happens if we slice off the slanted parts on the ends?

Let’s look at a parallelogram.

parallelogram3

Parallelogram

What happens if we slice off the slanted parts on the ends?

Let’s look at a parallelogram.

parallelogram4

Parallelogram

What happens if we slice off the slanted parts on the ends?

Let’s look at a parallelogram.

parallelogram5

Parallelogram

What happens if we slice off the slanted parts on the ends?

Let’s look at a parallelogram.

parallelogram6

Parallelogram

What happens if we slice off the slanted parts on the ends?

Let’s look at a parallelogram.

parallelogram7

Parallelogram

What happens if we slice off the slanted parts on the ends?

Let’s look at a parallelogram.

parallelogram8

Parallelogram

What happens if we slice off the slanted parts on the ends?

Let’s look at a parallelogram.

parallelogram9

Parallelogram

What happens if we slice off the slanted parts on the ends?

Let’s look at a parallelogram.

parallelogram10

Parallelogram

What happens if we slice off the slanted parts on the ends?

Let’s look at a parallelogram.

parallelogram11

Parallelogram

What happens if we slice off the slanted parts on the ends?

Let’s look at a parallelogram.

What will the area formula be now that it is a rectangle?

parallelogram12

Parallelogram

What happens if we slice off the slanted parts on the ends?

Let’s look at a parallelogram.

What will the area formula be now that it is a rectangle?

bh

parallelogram13

Parallelogram

bh

Be careful though! The height has to be perpendicular from the base, just like the side of a rectangle!

parallelogram14

Parallelogram

bh

Be careful though! The height has to be perpendicular from the base, just like the side of a rectangle!

parallelogram15

Parallelogram

bh

Be careful though! The height has to be perpendicular from the base, just like the side of a rectangle!

rhombus

Rhombus

bh

The rhombus is just a parallelogram with all equal sides! So it also has bh for an area formula.

practice2

Practice!

9 in

Parallelogram

3 in

Rhombus

2.7 cm

4 cm

answers2

Answers

9 in

Parallelogram

27 in2

3 in

Rhombus

2.7 cm

10.8 cm2

4 cm

let s try something new with the parallelogram1

Earlier, you saw that you could use two trapezoids to make a parallelogram.

Let’s try something new with the parallelogram.

let s try something new with the parallelogram2

Earlier, you saw that you could use two trapezoids to make a parallelogram.

Let’s try something new with the parallelogram.

Let’s try to figure out the formula since we now know the area formula for a parallelogram.

trapezoid2

Trapezoid

So we see that we are dividing the parallelogram in half. What will that do to the formula?

trapezoid3

Trapezoid

So we see that we are dividing the parallelogram in half. What will that do to the formula?

bh

trapezoid4

Trapezoid

So we see that we are dividing the parallelogram in half. What will that do to the formula?

bh

2

trapezoid5

Trapezoid

But now there is a problem.

What is wrong with the base?

bh

2

trapezoid6

Trapezoid

So we need to account for the split base, by calling the top base, base 1, and the bottom base, base 2. By adding them together, we get the original base from the parallelogram. The heights are the same, so no problem there.

bh

2

trapezoid7

Trapezoid

So we need to account for the split base, by calling the top base, base 1, and the bottom base, base 2. By adding them together, we get the original base from the parallelogram. The heights are the same, so no problem there.

base 2

base 1

base 2

base 1

(b1 + b2)h

2

practice3

Practice!

3 m

Trapezoid

5 m

11 m

answers3

Answers

3 m

Trapezoid

35 m2

5 m

11 m

summary so far19
Summary so far...

bh

bh

(b1 + b2)h

2

2

summary so far20
Summary so far...

bh

bh

(b1 + b2)h

2

2

summary so far21
Summary so far...

bh

bh

(b1 + b2)h

2

2

summary so far22
Summary so far...

bh

bh

(b1 + b2)h

2

2

summary so far23
Summary so far...

bh

bh

(b1 + b2)h

2

2

summary so far24
Summary so far...

bh

bh

(b1 + b2)h

2

2

so there is just one more left1

Let’s go back to the triangle.

A few weeks ago you learned that by reflecting a triangle, you can make a kite.

So there is just one more left!

slide79

Kite

Let’s go back to the triangle.

A few weeks ago you learned that by reflecting a triangle, you can make a kite.

So there is just one more left!

slide80

Kite

Now we have to determine the formula. What is the area of a triangle formula again?

slide81

Kite

Now we have to determine the formula. What is the area of a triangle formula again?

bh

2

slide82

Kite

Now we have to determine the formula. What is the area of a triangle formula again?

bh

2

Fill in the blank. A kite is made up of ____ triangles.

slide83

Kite

Now we have to determine the formula. What is the area of a triangle formula again?

bh

2

Fill in the blank. A kite is made up of ____ triangles.

So it seems we should multiply the formula by 2.

slide84

Kite

bh

bh

*2 =

2

slide85

Kite

bh

bh

*2 =

2

Now we have a different problem. What is the base and height of a kite? The green line is called the symmetry line, and the red line is half the other diagonal.

slide86

Kite

Let’s use kite vocabulary instead to create our formula.

Symmetry Line*Half the Other Diagonal

practice4

Practice!

Kite

2 ft

10 ft

answers4

Answers

Kite

20 ft2

2 ft

10 ft

summary so far39
Summary so far...

bh

bh

(b1 + b2)h

2

2

summary so far40
Summary so far...

bh

bh

(b1 + b2)h

2

2

summary so far41
Summary so far...

bh

bh

(b1 + b2)h

2

2

summary so far42
Summary so far...

bh

bh

(b1 + b2)h

2

2

summary so far43
Summary so far...

bh

bh

(b1 + b2)h

2

2

summary so far44
Summary so far...

bh

bh

(b1 + b2)h

2

2

summary so far45
Summary so far...

bh

bh

(b1 + b2)h

2

2

summary so far46
Summary so far...

bh

bh

(b1 + b2)h

2

2

summary so far47
Summary so far...

bh

bh

(b1 + b2)h

2

2

summary so far48
Summary so far...

bh

bh

(b1 + b2)h

2

2

Symmetry Line * Half the Other Diagonal

final summary make sure all your formulas are written down
Final SummaryMake sure all your formulas are written down!

bh

bh

(b1 + b2)h

2

2

Symmetry Line * Half the Other Diagonal

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