copyright©amberpasillas2010. perimeter – (p) (p) the distance around a figure. 10 ft. 6 ft. 10 6...


Perimeter – (P) The distance around a figure.

10 ft. 10 ft.

10 ft.

6 ft.

106

1010+

36 ft.


PERIMETER: Is the distance around a figure.

When you add the sides you are adding the units.

When you add units, your units DO NOT CHANGE!

If this rectangle has units in inches, then you are adding in + in + in + in = in

You must include units in every answer!


The Area of a figure is the number of square units needed to cover it.

A = 2 • 3

A = 6 square units

A = 6 units2 2

3

PERIMETER: Is the distance around a figure.

in + in + in + in = in

AREA: Is the square units that cover a figure.

length • width= in • in = in2

VOLUME: The number of cubic units inside a figure.

length • width • height in • in • in = in3

length

length width

height

squared

cubed

width



8 m

6 m

A = 8 • 62

= 24 m2

A = base • height 2

A triangle is half the area of a rectangle. To find the area of a triangle you use the rectangle formula and divide it in half.

bhA=

2

5 m


5 in

3 inA = b • h

A = 5 • 3 = 15 in2

To find the area for a parallelogram use what you know about area of a rectangle.

A = base • height4 in


6 ft

3 ft

A = (b1 + b2) • h2

4 ft

A = (3 + 6) • 42A = (9) • 4

2= 36

2 = 18 ft2

A = (base1 + base2) • height

25 ft


Take out your STUDY GUIDE


Perimeter & Area Review

# 11

The Area (A) of a figure is the number of square units needed to cover it.

The Perimeter (P) is the distance around a figure.

a

b

c P= a+b+c units

height

base

(h)(b)

A = 2 • 6

12 square units 12 units2

9 cm

5 cm 6 cm3 cm

Area & Perimeter of a Triangle

# 12

PerimeterP = a + b + c

P = 5 + 6 + 9

P = 20 cm

Area1A b h2

1A 9 32

1A 272

2A 13.5 cm



#13 Perimeter & Area of a Rectangle The Perimeter of a figure is the distance around a figure.

2 in. 2 in.

5 in.

5 in.

2525+

14 in.

2 2P l w

The Area of a figure is the number of square units needed to cover it.

A = 3 • 2

6 square units

6 units2

A b h 3

2


Teacher Note: The following study guide slides were taken from the lesson on Perimeter and Area review under the PERIMETER FOLDER


a

b

c

de

f

g

h P=a+b+c+d+e+f+g+h

a

b

cP= a+b+c

P=4ss

s

s

s

l

l

w w

P=2l+2w

#9


#10 Perimeter of a TrianglePerimeter: Distance around a geometric figure.

a 3 cm

c 7 cm

b 5 cm

P a b c

P 15 cmP 3 5 7

When you add thesides, you are alsoadding the units. When you add units,your UNITS DO NOTCHANGE!

You must include units in every answer!


#11 Perimeter of a Rectangle & SquareThe Perimeter of a figure is the distance around a figure.

2 in. 2 in.

5 in.

5 in.

2525+

14 in.

Rectangle

45

2 2P l w

2(5) 2(4)P

18 units

4P s8 ft

8 ft

4(8)P 32 ft

Square

10 8


Teacher Note: Extra lesson on just area

formulas without the perimeter


Area of a RectangleArea of a Square

Area of a Triangle

Area of a Parallelogram

Area of a Trapezoid

REVIEW OF FORMULAS


Area of a Rectangle

height

base

(h)

(b)

A = bh

The area of this rectangle is 8 squares, or 8 units squared

Area is in units2 because you are multiplying units.


A square is a special rectangle

Since the base and the height are the same size, we call them sides (s) instead of base and height.

sheight = s

s base = s

A= s2

Area of a Square


What is the area of the square?

4 m.

4 m.

44x

16 m.2

16 m2 or square meters

Area of a Square


Area of a TriangleGiven the formula for

area of a rectangle, we are going to use that information to

discover the formula for the area of a triangle.

Watch carefully not to miss it!


Area of a TriangleGiven a right triangle

Make a similar triangle,


Area of a TriangleGiven a right triangle

Make a similar triangle, flip it and put both triangles next to each other

What polygon is this?

A Rectangle


Area of a Triangle

What is the formula for the area of a triangle?

We can use the formula for area of a rectangle to find the formula for area of a triangle.

bA=

2

hA=b h

Two triangles make one rectangle.

We want to find half of the area of the rectangle.

We since we are

finding of the area.

÷2

half

base

height

b

h


Area of a Triangle

base

heighth

This holds true for any triangle

b hA=

2

Notice when we put two right triangles together

it made a rectangle. When we put two isosceles

triangles together it made a parallelogram.

We are still finding half the area so we divide by 2.


Draw a straight line from the top corner perpendicular to the base

Cut that triangle and move it to the other sideWhat shape does it make?

Rectangle

Area for a Parallelogram


What is the formula for area of a parallelogram?

A parallelogram has the same area as a rectangle

h

base = b

height = h h

b

A=b h



4 cm.90º

2 cm.

= 8 cm.2

Check to see if you got it right.

A=b h

A=4 2



4 cm.90º

2 cm.

= 8 cm.2

A=b h

A=4 2

Cut off the piece at the dotted line.



4 cm.90º

2 cm.

= 8 cm.2

A=b h

A=4 2

Move this piece to the other side.



4 cm.90º

2 cm.

= 8 cm.2

A=b h

A=4 2

Now you have a rectangle

A = 8 square cm. or 8 cm.2

Let’s check it with the area of a rectangle.

How many squares do you see?



b1

b2

h

Copy that trapezoid, flip it over, and put it next to the original

b1

b2

h

Given the height, base 1, and base 2

(b1 + b2)

h

What shape is it now?

Parallelogram

Area of a Trapezoid


Notice that the trapezoid is half the area of the parallelogram. It takes two trapezoids to make one parallelogram.

(b1 + b2)

h

Given our original trapezoid Put together with a similar flipped trapezoid, we found it made a parallelogram.

We are going to use the area of a parallelogram to find the area of a trapezoid.

Area of a Trapezoid


(b1 + b2)

h

Parallelogram Trapezoid

A = (b1 + b2)

2

A=b h h

Area of a Trapezoid


Area of Trapezoid

A = (b1 + b2) 2

2 in

6 in

3 in

= 12 in2

h

(2 6) 3A

2

(8) 3

2

24

2

Area of a Trapezoid


Area of a Trapezoid

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