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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

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**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

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**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

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**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

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**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

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**Chapter 1 / Whole Numbers and Introduction to Algebra**

Given a circle of radius, r, the circumference is C = 2 r. Martin-Gay, Prealgebra, 5ed

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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**Chapter 1 / Whole Numbers and Introduction to Algebra**

Cube side side side Volume = side side side V = s3 SA = 6s3 Martin-Gay, Prealgebra, 5ed

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**Chapter 1 / Whole Numbers and Introduction to Algebra**

Sphere radius Volume = Martin-Gay, Prealgebra, 5ed

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**Chapter 1 / Whole Numbers and Introduction to Algebra**

Circular Cylinder height radius Volume = V = r2h SA = 2 r h + 2r2 Martin-Gay, Prealgebra, 5ed

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**Chapter 1 / Whole Numbers and Introduction to Algebra**

Cone height radius Volume =

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**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

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**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

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