Area Formulas Rectangle What is the area formula?

Area FormulasArea Formulas

Rectangle

Rectangle

What is the area formula?

Rectangle

What is the area formula? bh

Rectangle


What other shape has 4 right angles?

Rectangle



Square!

Rectangle



Square!

Can we use the same

area formula?

Rectangle



Square!

Can we use the same

area formula? Yes

Practice!Practice!Rectangle

Square

10m

17m

14cm

AnswersAnswersRectangle

Square

10m

17m

14cm

196 cm2

170 m2

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

What shape is made?

TriangleSo then what happens if we

cut a rectangle in half?

What shape is made?



What shape is made?2 Triangles




So then what happens to the formula?





bh





bh2

Practice!Practice!Triangle

5 ft

14 ft

AnswersAnswers

35 ft2Triangle5 ft

14 ft

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

bh


bh bh


bh bh2

ParallelogramLet’s look at a parallelogram.


What happens if we slice off the slanted parts on the

ends?



ends?What will the area formula

be now that it is a rectangle?



ends?What will the area formula

be now that it is a rectangle?

bh

ParallelogramBe careful though! The

height has to be perpendicular from the

base, just like the side of a rectangle!

bh

RhombusThe rhombus is just a parallelogram with all equal sides! So it also

has bh for an area formula.

bh

Practice!Practice!Parallelogram

Rhombus

3 in

9 in

4 cm

2.7 cm

AnswersAnswers

10.8 cm2

27 in2Parallelogram

Rhombus

3 in

9 in

4 cm

2.7 cm

Let’s try something new with the parallelogram.


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


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

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

Trapezoid

TrapezoidSo we see that

we are dividing the

parallelogram in half. What will that do to the formula?


we are dividing the


bh


we are dividing the


bh2

TrapezoidBut now there is a problem.

What is wrong with the base?

bh2

Trapezoid

bh2

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.

Trapezoid

(b1 + b2)h2

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 1

base 2

Practice!Practice!Trapezoid

11 m

3 m

5 m

AnswersAnswers

35 m2Trapezoid

11 m

3 m

5 m


bh


bh bh


bh bh2


bh bh2

(b1 + b2)h2

So there is just one more left!

So there is just one more left!

Let’s go back to the triangle.

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

KiteSo there is just one

more left!

Let’s go back to the triangle.

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

KiteNow we have to

determine the formula. What is

the area of a triangle formula again?

KiteNow we have to



bh2

KiteNow we have to



bh2

Fill in the blank. A kite is made up of

____ triangles.

KiteNow we have to



bh2

Fill in the blank. A kite is made up of

____ triangles.

So it seems we should multiply the

formula by 2.

Kite

bh2

*2 = bh

Kite

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.

bh2

*2 = bh

KiteLet’s use kite

vocabulary instead to create our formula.

Symmetry Line*Half the Other Diagonal

Practice!Practice!Kite

2 ft

10 ft

AnswersAnswers

20 ft2Kite2 ft

10 ft


bh


bh bh


bh bh2


bh bh2

(b1 + b2)h2


bh bh2

(b1 + b2)h2

Symmetry Line * Half the Other Diagonal

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

down!down!

bh bh2

(b1 + b2)h2

Symmetry Line * Half the Other Diagonal

Area Formulas Rectangle What is the area formula?

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