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Area Formulas

Rectangle

Rectangle

- What is the area formula?

Rectangle

- What is the area formula?

bh

Rectangle

- What is the area formula?

bh

What other shape has 4 right angles?

Rectangle

- What is the area formula?

bh

Square!

What other shape has 4 right angles?

Rectangle

- What is the area formula?

bh

Square!

What other shape has 4 right angles?

Can we use the same area formula?

Rectangle

- What is the area formula?

bh

Square!

What other shape has 4 right angles?

Can we use the same area formula?

Yes

Practice!

17m

Rectangle

10m

Square

14cm

Answers

17m

Rectangle

10m

170 m2

Square

196 cm2

14cm

- So then what happens if we cut a rectangle in

half? - What shape is made?

Triangle

- So then what happens if we cut a rectangle in

half? - What shape is made?

Triangle

- So then what happens if we cut a rectangle in

half? - What shape is made?

2 Triangles

Triangle

- So then what happens if we cut a rectangle in

half? - What shape is made?

2 Triangles

So then what happens to the formula?

Triangle

- So then what happens if we cut a rectangle in

half? - What shape is made?

2 Triangles

So then what happens to the formula?

Triangle

- So then what happens if we cut a rectangle in

half? - What shape is made?

2 Triangles

bh

So then what happens to the formula?

Triangle

- So then what happens if we cut a rectangle in

half? - What shape is made?

2 Triangles

bh

2

So then what happens to the formula?

Practice!

Triangle

14 ft

5 ft

Answers

Triangle

35 ft2

14 ft

5 ft

Summary so far...

- bh

Summary so far...

- bh

Summary so far...

- bh

Summary so far...

- bh

bh

Summary so far...

- bh

bh

2

Parallelogram

- Lets look at a parallelogram.

Parallelogram

- Lets look at a parallelogram.

What happens if we slice off the slanted parts on

the ends?

Parallelogram

- Lets look at a parallelogram.

What happens if we slice off the slanted parts on

the ends?

Parallelogram

- Lets look at a parallelogram.

What happens if we slice off the slanted parts on

the ends?

Parallelogram

- Lets look at a parallelogram.

What happens if we slice off the slanted parts on

the ends?

Parallelogram

- Lets look at a parallelogram.

What happens if we slice off the slanted parts on

the ends?

Parallelogram

- Lets look at a parallelogram.

What happens if we slice off the slanted parts on

the ends?

Parallelogram

- Lets look at a parallelogram.

What happens if we slice off the slanted parts on

the ends?

Parallelogram

- Lets look at a parallelogram.

What happens if we slice off the slanted parts on

the ends?

Parallelogram

- Lets look at a parallelogram.

What happens if we slice off the slanted parts on

the ends?

Parallelogram

- Lets look at a parallelogram.

What happens if we slice off the slanted parts on

the ends?

Parallelogram

- Lets look at a parallelogram.

What happens if we slice off the slanted parts on

the ends?

What will the area formula be now that it is a

rectangle?

Parallelogram

- Lets look at a parallelogram.

What happens if we slice off the slanted parts on

the ends?

What will the area formula be now that it is a

rectangle?

bh

Parallelogram

- Be careful though! The height has to be

perpendicular from the base, just like the side

of a rectangle!

bh

Parallelogram

- Be careful though! The height has to be

perpendicular from the base, just like the side

of a rectangle!

bh

Parallelogram

- Be careful though! The height has to be

perpendicular from the base, just like the side

of a rectangle!

bh

Rhombus

- The rhombus is just a parallelogram with all

equal sides! So it also has bh for an area

formula.

bh

Practice!

9 in

Parallelogram

3 in

Rhombus

2.7 cm

4 cm

Answers

9 in

27 in2

Parallelogram

3 in

10.8 cm2

Rhombus

2.7 cm

4 cm

- Lets try something new with the parallelogram.

- Lets try something new with the parallelogram.

Earlier, you saw that you could use two

trapezoids to make a parallelogram.

- Lets try something new with the parallelogram.

Earlier, you saw that you could use two

trapezoids to make a parallelogram.

Lets try to figure out the formula since we now

know the area formula for a parallelogram.

Trapezoid

Trapezoid

Trapezoid

- So we see that we are dividing the parallelogram

in half. What will that do to the formula?

Trapezoid

- So we see that we are dividing the parallelogram

in half. What will that do to the formula?

bh

Trapezoid

- So we see that we are dividing the parallelogram

in half. What will that do to the formula?

bh

2

Trapezoid

- But now there is a problem.
- What is wrong with the base?

bh

2

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

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

Practice!

3 m

Trapezoid

5 m

11 m

Answers

3 m

Trapezoid

35 m2

5 m

11 m

Summary so far...

- bh

Summary so far...

- bh

Summary so far...

- bh

Summary so far...

- bh

bh

Summary so far...

- bh

bh

2

Summary so far...

- bh

bh

2

Summary so far...

- bh

bh

2

Summary so far...

- bh

bh

2

Summary so far...

- bh

bh

2

Summary so far...

- bh

bh

2

Summary so far...

- bh

bh

2

Summary so far...

- bh

bh

2

Summary so far...

- bh

bh

2

Summary so far...

- bh

bh

2

Summary so far...

- bh

bh

(b1 b2)h

2

2

Summary so far...

- bh

bh

(b1 b2)h

2

2

Summary so far...

- bh

bh

(b1 b2)h

2

2

Summary so far...

- bh

bh

(b1 b2)h

2

2

Summary so far...

- bh

bh

(b1 b2)h

2

2

Summary so far...

- bh

bh

(b1 b2)h

2

2

- So there is just one more left!

- So there is just one more left!

Lets go back to the triangle. A few weeks ago

you learned that by reflecting a triangle, you

can make a kite.

Kite

- So there is just one more left!

Lets go back to the triangle. A few weeks ago

you learned that by reflecting a triangle, you

can make a kite.

Kite

- Now we have to determine the formula. What is

the area of a triangle formula again?

Kite

- Now we have to determine the formula. What is

the area of a triangle formula again?

bh

2

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.

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.

Kite

bh

bh

2

2

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.

Kite

- Lets use kite vocabulary instead to create our

formula.

Symmetry LineHalf the Other Diagonal

Practice!

Kite

2 ft

10 ft

Answers

Kite

20 ft2

2 ft

10 ft

Summary so far...

- bh

Summary so far...

- bh

Summary so far...

- bh

Summary so far...

- bh

bh

Summary so far...

- bh

bh

2

Summary so far...

- bh

bh

2

Summary so far...

- bh

bh

2

Summary so far...

- bh

bh

2

Summary so far...

- bh

bh

2

Summary so far...

- bh

bh

2

Summary so far...

- bh

bh

2

Summary so far...

- bh

bh

2

Summary so far...

- bh

bh

2

Summary so far...

- bh

bh

2

Summary so far...

- bh

bh

(b1 b2)h

2

2

Summary so far...

- bh

bh

(b1 b2)h

2

2

Summary so far...

- bh

bh

(b1 b2)h

2

2

Summary so far...

- bh

bh

(b1 b2)h

2

2

Summary so far...

- bh

bh

(b1 b2)h

2

2

Summary so far...

- bh

bh

(b1 b2)h

2

2

Summary so far...

- bh

bh

(b1 b2)h

2

2

Summary so far...

- bh

bh

(b1 b2)h

2

2

Summary so far...

- bh

bh

(b1 b2)h

2

2

Summary so far...

- bh

bh

(b1 b2)h

2

2

Symmetry Line Half the Other Diagonal

Final SummaryMake sure all your formulas are

written down!

- bh

bh

(b1 b2)h

2

2

Symmetry Line Half the Other Diagonal