1. Area, Volume, and Surface Area
Chapter 1 / Whole Numbers and Introduction to Algebra
Section 9.3
Area, Volume, and Surface Area

2. Chapter 1 / Whole Numbers and Introduction to Algebra
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 units2
A = 6 units2 2 3

3. Chapter 1 / Whole Numbers and Introduction to Algebra
Area Formulas
Parallelogram
Triangle 3 2 2 3
3 • 2 = 6
A = lw
Rectangle 3 2
The diagonal of
a parallelogram
forms 2
congruent triangles. 3 2
(3 • 2) = 3
3 • 2 = 6 1
A = bh 2
A = bh
Martin-Gay, Prealgebra, 5ed

4. Chapter 1 / Whole Numbers and Introduction to Algebra
More Area Formulas
Trapezoid B
Square
side h b +
area = side • side
A = s • s = s 2
Martin-Gay, Prealgebra, 5ed

5. 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

6. Chapter 1 / Whole Numbers and Introduction to Algebra
Given a circle of radius, r, the circumference is C = 2 r.
Martin-Gay, Prealgebra, 5ed

7. Martin-Gay, Prealgebra, 5ed
Dividing the circle into 4 equal sectors, half the circumference, r, is blue and the other half is red. r r
8 equal sectors r r
Area of a Circle
16 equal sectors r r
32 equal sectors r r
Martin-Gay, Prealgebra, 5ed

8. Notice the rectangular shape. Martin-Gay, Prealgebra, 5ed
64 equal sectors r r
128 equal sectors r r
Area of a Circle
equal sectors n 2 r r
Notice the rectangular shape.
A = lw
A = (r)r
A = r 2
Martin-Gay, Prealgebra, 5ed

9. Chapter 1 / Whole Numbers and Introduction to Algebra
Perimeter/ Circumference
Plane Figure
Drawing
Area
P = a + b + c
Triangle
Parallelogram
P = a + b + c + d
A = bh
Rectangle
P = 2l + 2w
A = lw
Square
P = 4s
A = s2
P = a + b + c + d
Trapezoid
C =  d or 2 r
A = r 2
Circle
Martin-Gay, Prealgebra, 5ed

10. Chapter 1 / Whole Numbers and Introduction to Algebra
Volume
Volume 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 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

11. Chapter 1 / Whole Numbers and Introduction to Algebra
Surface Area
A polyhedron is a solid formed by the intersection of a finite number of planes.
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

12. Chapter 1 / Whole Numbers and Introduction to Algebra
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

13. Chapter 1 / Whole Numbers and Introduction to Algebra
Rectangular Solid
height
width
length
Volume = length  width  height
V = lwh
SA = 2lh + 2wh + 2lw
Martin-Gay, Prealgebra, 5ed

14. Chapter 1 / Whole Numbers and Introduction to Algebra
Cube
side
side
side
Volume = side  side  side
V = s3
SA = 6s3
Martin-Gay, Prealgebra, 5ed

15. Chapter 1 / Whole Numbers and Introduction to Algebra
Sphere
radius
Volume =
Martin-Gay, Prealgebra, 5ed

16. Chapter 1 / Whole Numbers and Introduction to Algebra
Circular Cylinder
height
radius
Volume =
V = r2h
SA = 2 r h + 2r2
Martin-Gay, Prealgebra, 5ed

17. Chapter 1 / Whole Numbers and Introduction to Algebra
Cone
height
radius
Volume =

18. Square-Based Pyramid 1 3 ( ) side height Volume = V = 1 3 s2h height( )
side
height
Volume =
V = 1 3
s2h
B = area of base,
p = perimeter,
l = slant height

19. Martin-Gay, Prealgebra, 5ed
Helpful Hint
Volume is always measured in cubic units.
Surface area is always measured in square units.
Martin-Gay, Prealgebra, 5ed