Area volume and surface area
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Section 9.3. Area, Volume, and Surface Area. Area of a Rectangle. Area is measured in square units. A square unit is a square one unit on each side. For example, start with a rectangle with length ( l ) 3 units and width ( w ) 2 units. A = l • w A = 3 • 2 units 2 A = 6 units 2. 2.

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Area, Volume, and Surface Area

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Area volume and surface area

Section 9.3

Area, Volume, and Surface Area


Area volume and surface area

Area of a Rectangle

Areais measured in square units. A square unit is a square one unit on each side.

For example, start with a rectangle with length (l) 3 units and width (w) 2 units.

A=l•w

A= 3•2 units2

A= 6 units2

2

3


Area volume and surface area

2

2

Rectangle

2

3

2

3

3•2=6

A=lw

3

3

(3•2) = 3

1

A=bh

2

Area Formulas

Parallelogram

Triangle

The diagonal of

a parallelogram

forms 2

congruent triangles.

3•2 = 6

A=bh

Martin-Gay, Prealgebra, 5ed


Area volume and surface area

B

Square

h

b

B

b

side

side

h

More Area Formulas

Trapezoid

+

area=side •side

A=s•s=s2

Martin-Gay, Prealgebra, 5ed


Area volume and surface area

Helpful Hint

Area is always measured in square units.

When finding the area of figures, check to make sure that all measurements are the same units before calculations are made.

Martin-Gay, Prealgebra, 5ed


Area volume and surface area

r

Given a circle of radius, r,the circumference isC= 2r.

Martin-Gay, Prealgebra, 5ed


Area volume and surface area

Dividing the circle into 4 equal sectors, half the circumference, r, is blue and the other half is red.

8 equal sectors

r

r

r

r

r

r

16 equal sectors

32 equal sectors

r

r

r

r

r

r

Area of a Circle

Martin-Gay, Prealgebra, 5ed


Area volume and surface area

64 equal sectors

128 equal sectors

r

r

r

r

r

r

n

2

equal sectors

r

r

r

Area of a Circle

Notice the rectangular shape.

A = lw

A = (r)r

A =r2

Martin-Gay, Prealgebra, 5ed


Area volume and surface area

Perimeter/ Circumference

Plane Figure

Drawing

Area

P=a+ b+c

Triangle

P=a+b+c+d

Parallelogram

A=bh

P = 2l+ 2w

Rectangle

A=lw

Square

P= 4s

A=s2

P=a+b+c+d

Trapezoid

C=d or 2r

A=r2

Circle

Martin-Gay, Prealgebra, 5ed


Area volume and surface area

Volumemeasures the number of cubic units that fill the space of a solid. The volume of a box or can is the amount of space inside.

Volume

Volume can be used to describe the amount of juice in a pitcher or the amount of concrete needed to pour a foundation for a house.

Martin-Gay, Prealgebra, 5ed


A polyhedron is a solid formed by the intersection of a finite number of planes

A polyhedron is a solid formed by the intersection of a finite number of planes.

Surface Area

The surface area of a polyhedron is the sum of the areas of the faces of the polyhedron.

Surface area is measured in square units.

Martin-Gay, Prealgebra, 5ed


Area volume and surface area

The volume of a solid is the number of cubic units in the solid.

1 inch

1 centimeter

1 centimeter

1 inch

1 centimeter

1 inch

1 cubic centimeter

1 cubic inch

Martin-Gay, Prealgebra, 5ed


Rectangular solid

Rectangular Solid

height

width

length

Volume =lengthwidth height

V=lwh

SA = 2lh + 2wh + 2lw

Martin-Gay, Prealgebra, 5ed


Area volume and surface area

Cube

side

side

side

Volume =sidesideside

V= s3

SA= 6s3

Martin-Gay, Prealgebra, 5ed


Sphere

Sphere

radius

Volume =

Martin-Gay, Prealgebra, 5ed


Circular cylinder

Circular Cylinder

height

radius

Volume=

V=r2h

SA= 2rh + 2r2

Martin-Gay, Prealgebra, 5ed


Area volume and surface area

Cone

height

radius

Volume =


Square based pyramid

1

2

side

height

(

)

·

·

3

1

V=

s2h

3

Square-Based Pyramid

height

side

Volume =

B = area of base,

p = perimeter,

l = slant height


Area volume and surface area

Helpful Hint

Volume is always measured in cubic units.

Surface area is always measured in square units.

Martin-Gay, Prealgebra, 5ed


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