Section 9 3 Area Volume and Surface Area

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 2 3 A = 3 • 2 units 2 A = 6 units 2 2

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

More Area Formulas Trapezoid B Square h side B side b + b area = side • side A = s • s = s 2 h Martin-Gay, Prealgebra, 5 ed 4

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, 5 ed 5

r Given a circle of radius, r, the circumference is C = 2 r. Martin-Gay, Prealgebra, 5 ed 6

Area of a Circle Martin-Gay, Prealgebra, 5 ed 7

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

Plane Figure Triangle Parallelogram Rectangle Square Trapezoid Circle Drawing Perimeter/ Circumference Area P=a+b+c+d A = bh P = 2 l + 2 w A = lw P = 4 s A = s 2 P=a+b+c+d C = d or 2 r Martin-Gay, Prealgebra, 5 ed A = r 2 9

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, 5 ed 10

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, 5 ed 11

The volume of a solid is the number of cubic units in the solid. 1 inch 1 centimeter 1 cubic centimeter 1 inch 1 cubic inch Martin-Gay, Prealgebra, 5 ed 12

Rectangular Solid height width length Volume = length width height V = lwh SA = 2 lh + 2 wh + 2 lw Martin-Gay, Prealgebra, 5 ed 13

Cube side Volume = side V = s 3 SA = 6 s 3 Martin-Gay, Prealgebra, 5 ed 14

Sphere radius Volume = Martin-Gay, Prealgebra, 5 ed 15

Circular Cylinder height radius Volume = V = r 2 h SA = 2 r h + 2 r 2 Martin-Gay, Prealgebra, 5 ed 16

Cone height radius Volume = 17

Square-Based Pyramid height side 1 (side )2 height Volume = 3 1 V = s 2 h 3 B = area of base, p = perimeter, l = slant height 18

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