# Area, Volume, and Surface Area - PowerPoint PPT Presentation

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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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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

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

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 2r

A=r2

Circle

Martin-Gay, Prealgebra, 5ed

### 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.

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

### Rectangular Solid

height

width

length

Volume =lengthwidth height

V=lwh

SA = 2lh + 2wh + 2lw

Martin-Gay, Prealgebra, 5ed

### Cube

side

side

side

Volume =sidesideside

V= s3

SA= 6s3

Martin-Gay, Prealgebra, 5ed

### Sphere

Volume =

Martin-Gay, Prealgebra, 5ed

### Circular Cylinder

height

Volume=

V=r2h

SA= 2rh + 2r2

Martin-Gay, Prealgebra, 5ed

height

Volume =

1

2

side

height

(

)

·

·

3

1

V=

s2h

3

### Square-Based Pyramid

height

side

Volume =

B = area of base,

p = perimeter,

l = slant height