Area Formulas (1)

8/7/2019 Area Formulas (1)

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Area FormulasArea Formulas


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Rectangle


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Rectangle

What is the area formula?


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Rectangle

What is the area formula? bh


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Rectangle


What other shape has 4 right angles?


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Rectangle


What other shape has 4 right angles? Square!


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Rectangle



Can we use the same

area formula?


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Rectangle



Can we use the same

area formula?Yes


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Practice!Practice!

Rectangle

Square

10m

17m

14cm


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AnswersAnswers

Rectangle

Square

10m

17m

14cm

196 cm2

170 m2


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So then what happens if we

cut a rectangle in half?

What shape is made?


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Triangle



What shape is made?


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Triangle



What shape is made?2 Triangles


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Triangle




So then what happens tothe formula?


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Triangle






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Triangle





bh


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Triangle





bh2


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AnswersAnswers

35 ft2Triangle

5 ft

14 ft


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Summary so far...Summary so far...bh


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Summary so far...Summary so far...bh bh


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Summary so far...Summary so far...bh bh

2


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Parallelogram

Lets look at a

parallelogram.


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Parallelogram

Lets look at a

parallelogram.

What happens if we slice

off the slanted parts on the

ends?


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Parallelogram

Lets look at a

parallelogram.



ends?


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Parallelogram

Lets look at a

parallelogram.



ends?


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Parallelogram

Lets look at a

parallelogram.



ends?


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Parallelogram

Lets look at a

parallelogram.



ends?


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Parallelogram

Lets look at a

parallelogram.



ends?


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Parallelogram

Lets look at a

parallelogram.



ends?


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Parallelogram

Lets look at a

parallelogram.



ends?


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Parallelogram

Lets look at a

parallelogram.



ends?


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Parallelogram

Lets look at a

parallelogram.



ends?

What will the area formulabe now that it is a

rectangle?


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Parallelogram

Lets look at a

parallelogram.



ends?

What will the area formulabe now that it is a

rectangle?bh


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Parallelogram

Be careful though! The

height has to be

perpendicular from thebase, just like the side of

a rectangle!

bh


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Parallelogram


height has to be


a rectangle!

bh


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Parallelogram


height has to be


a rectangle!

bh


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Rhombus

The rhombus is just a

parallelogram with all

equal sides! So it alsohas bh for an area

formula.

bh


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Practice!Practice!

Parallelogram

Rhombus

3 in

9 in

4 cm

2.7 cm


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AnswersAnswers

10.8 cm

2

27 in2Parallelogram

Rhombus

3 in

9 in

4 cm

2.7 cm


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Lets try something new

with the parallelogram.


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Earlier, you saw that youcould use two trapezoids to

make a parallelogram.


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Earlier, you saw that youcould use two trapezoids to

make a parallelogram.

Lets try to figure out theformula since we now

know the area formula for a

parallelogram.


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Trapezoid


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Trapezoid


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Trapezoid

So we see that

we are

dividing the

parallelogram

in half. What

will that do to

the formula?

bh


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Trapezoid

So we see that

we are

dividing the

parallelogram

in half. What

will that do to

the formula?

bh

2


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Trapezoid

But now there

is a problem.

What is wrongwith the base?

bh

2


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Trapezoid

bh

2

So we need to account

for the split base, by

calling the top base,

base 1, and the bottombase, base 2. By

adding them together,

we get the original base

from the parallelogram.

The heights are the

same, so no problem

there.


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Trapezoid

(b1 +b2)h

2

So we need to account

for the split base, by

calling the top base,

base 1, and the bottombase, 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 1

base 2


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Practice!Practice!

Trapezoid

11 m

3 m

5 m


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AnswersAnswers

35 m2Trapezoid

11 m

3 m

5 m


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Summary so far...Summary so far...

bh


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bh


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bh


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bh bh


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bh bh2


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bh bh2


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bh bh2


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bh bh2


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bh bh2


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bh bh2


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bh bh2


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bh bh2


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bh bh2


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bh bh2


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bh bh2

(b1 +b2)h2


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bh bh2

(b1 +b2)h2


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bh bh2

(b1 +b2)h2


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bh bh2

(b1 +b2)h2


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bh bh2

(b1 +b2)h2


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bh bh2

(b1 +b2)h2


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So there is just one

more left!


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more left!

Lets go back to thetriangle.

A few weeks ago

you learned that byreflecting a triangle,

you can make a kite.


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Kite


more left!

Lets go back to thetriangle.

A few weeks ago

you learned that byreflecting a triangle,

you can make a kite.


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Kite

Now we have to

determine the

formula. What is

the area of a triangle

formula again?


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Kite

Now we have to

determine the

formula. What is


formula again?bh

2


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Kite

Now we have to

determine the

formula. What is


formula again?bh

2

Fill in the blank. Akite is made up of

____ triangles.


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Kite

Now we have to

determine the

formula. What is


formula again?bh

2

Fill in the blank. Akite is made up of

____ triangles.

So it seems we

should multiply the

formula by 2.


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Kite

bh2

*2 =bh


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Kite

Now we have a different problem. What is

the base and height of a kite? The greenline is called the symmetry line, and the red

line is half the other diagonal.

bh2

*2 =bh


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Kite

Lets use kite

vocabulary instead to

create our formula.

Symmetry Line*Half the Other Diagonal

P i !P i !


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Practice!Practice!

Kite2 ft

10 ft

AA


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AnswersAnswers

20 ft2Kite 2 ft

10 ft


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bh


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bh


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bh


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bh bh


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bh bh2


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bh bh2


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S

ummary so far...S

ummary so far...bh bh

2


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S

ummary so far...S


2


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S

ummary so far...S


2


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S

ummary so far...S


2


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S

ummary so far...S


2


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S

ummary so far...S


2


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S

ummary so far...S


2


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S

ummary so far...S


2


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S

ummary so far...S


2(b1 +b2)h

2


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S

ummary so far...S


2(b1 +b2)h

2


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S

ummary so far...S


2(b1 +b2)h

2


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S

ummary so far...S


2(b1 +b2)h

2


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S

ummary so far...S


2(b1 +b2)h

2


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S

ummary so far...S


2(b1 +b2)h

2


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S

ummary so far...S


2(b1 +b2)h

2


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S

ummary so far...S


2(b1 +b2)h

2


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S

ummary so far...S


2(b1 +b2)h

2


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S

ummary so far...S


2(b1 +b2)h

2

Symmetry Line * Halfthe Other Diagonal

Final SummaryFinal Summary


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Final SummaryFinal SummaryMake sure all your formulas are written down!Make sure all your formulas are written down!

bh bh2

(b1 +b2)h2

Symmetry Line * Halfthe Other Diagonal

Area Formulas (1)

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