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Area, Volume, and Surface Area

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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= 2r.

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

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

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 2r

A=r2

Circle

Martin-Gay, Prealgebra, 5ed

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

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 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

height

width

length

Volume =lengthwidth height

V=lwh

SA = 2lh + 2wh + 2lw

Martin-Gay, Prealgebra, 5ed

side

side

side

Volume =sidesideside

V= s3

SA= 6s3

Martin-Gay, Prealgebra, 5ed

radius

Volume =

Martin-Gay, Prealgebra, 5ed

height

radius

Volume=

V=r2h

SA= 2rh + 2r2

Martin-Gay, Prealgebra, 5ed

height

radius

Volume =

1

2

side

height

(

)

·

·

3

1

V=

s2h

3

height

side

Volume =

B = area of base,

p = perimeter,

l = slant height

Helpful Hint

Volume is always measured in cubic units.

Surface area is always measured in square units.

Martin-Gay, Prealgebra, 5ed