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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

Section 9.3

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


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


B

Square

h

b

B

b

side

side

h

More Area Formulas

Trapezoid

+

area=side •side

A=s•s=s2

Martin-Gay, Prealgebra, 5ed


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


r

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

Martin-Gay, Prealgebra, 5ed


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


64 equal sectors circumference,

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


Perimeter/ Circumference 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


Volume circumference, measures 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 circumference, 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


The volume of a solid is the number of circumference, 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 circumference,

height

width

length

Volume =lengthwidth height

V=lwh

SA = 2lh + 2wh + 2lw

Martin-Gay, Prealgebra, 5ed


Cube circumference,

side

side

side

Volume =sidesideside

V= s3

SA= 6s3

Martin-Gay, Prealgebra, 5ed


Sphere
Sphere circumference,

radius

Volume =

Martin-Gay, Prealgebra, 5ed


Circular cylinder
Circular Cylinder circumference,

height

radius

Volume=

V=r2h

SA= 2rh + 2r2

Martin-Gay, Prealgebra, 5ed


Cone circumference,

height

radius

Volume =


Square based pyramid

1 circumference,

2

side

height

(

)

·

·

3

1

V=

s2h

3

Square-Based Pyramid

height

side

Volume =

B = area of base,

p = perimeter,

l = slant height


Helpful Hint circumference,

Volume is always measured in cubic units.

Surface area is always measured in square units.

Martin-Gay, Prealgebra, 5ed


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