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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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slide2
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

slide3
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

slide4
B

Square

h

b

B

b

side

side

h

More Area Formulas

Trapezoid

+

area=side •side

A=s•s=s2

Martin-Gay, Prealgebra, 5ed

slide5
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

slide6
r

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

Martin-Gay, Prealgebra, 5ed

slide7
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

slide8
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

slide9
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

slide10
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

slide12
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

slide14
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

slide17
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

slide19
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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