# Area, Volume, and Surface Area

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Chapter 1 / Whole Numbers and Introduction to Algebra

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

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