Area, Volume, and Surface Area

Area, Volume, and Surface Area, Volume, and Surface AreaArea

Section 9.3

Area of a RectangleArea of a Rectangle

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

2

3

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

A l • w

A 3 • 2 units2

A 6 units22

3 • 2 6 A bh

The diagonal of

a parallelogram

forms 2

congruent triangles.

3

2

2

3

3 • 2 6

A lw

RectangleRectangle

3

2

TriangleTriangle

Area Area FormulasFormulas

1A bh2

(3 • 2) 3 1

2

ParallelogramParallelogram

3

2

3Martin-Gay, Prealgebra, 5ed

area side • side

A s • s s

2

More Area More Area FormulasFormulas

B

B

bb+

h

h

SquareSquare

side

side

TrapezoidTrapezoid

1( )

2B b

1( )

2A B b


AreaArea is always measured in square units. is always measured in square units.

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

Helpful HintHelpful Hint


r

Given a circle of radius, Given a circle of radius, r,, the the circumference iscircumference is C 2 r.


Area of a CircleArea of a Circle


Notice the rectangular shape.

A lw

A (r)r

A r

2

equal sectorsn

2

r

r

r

64 equal sectors

r

r

r

128 equal sectors

r

r

r

Area of a CircleArea of a Circle


P a b c

P a b c d

P 2l 2w

P 4s

P a b c d

Plane Figure DrawingPerimeter/

Circumference Area

Triangle

Parallelogram

Rectangle

Square

Trapezoid

Circle C d or 2 r

A bh

A lw

A s2

A r 2

1( )

2A B b h

1

2A bh


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

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

VolumeVolume


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

Surface AreaSurface Area

11

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

Surface area is measured in square units.Surface area is measured in square units.

Martin-Gay, Prealgebra, 5ed

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

1 centimeter1 centimeter

1 centimeter

1 inch1 inch

1 inch

1 cubic centimeter 1 cubic inch


Rectangular SolidRectangular Solid

length

widthheight

Volume length width height

V = lwh

SA = 2lh + 2wh + 2lw


CubeCube

sideside

side

Volume = side side side

V = s3

SA = 6s3


SphereSphere

3( adi4

r3

us) Volume

radius

34

3V r

15

24SA r


Circular CylinderCircular Cylinder

Volume

V r2h

radius

height

2( adius) ( ht)r heig

16

SA 2 r h + 2r2


ConeCone

Volume

radius

height

21

3V r h

2( adius) (1

r hei3

ght)

17 2 2 2S hA r rr

Square-Based PyramidSquare-Based Pyramid

Volume

height

side13

2 ( )side height

V = 13

s2h

18

1

2SA B pl

B = area of base, p = perimeter, l = slant height

Helpful HintHelpful Hint

Volume is always measured in Volume is always measured in cubic unitscubic units..

19

Surface area is always measured in Surface area is always measured in square square unitsunits..


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Area, Volume, and Surface Area