Chapter 8

8-1 Estimating Perimeter and Area  Perimeter – total distance around the figure  Area – number of square units a figure encloses

8-1 Estimating Perimeter and Area-answers  Perimeter – total distance around the figure  Area – number of square units a figure encloses 12ft ; truck cab quite tall 8 in; book is not very wide 8 in; pizza not very big 2ft ; bathtub is not very deep

8-1 Estimating Perimeter and Area

8-1 Estimating Perimeter and Area-answers 10 yd 12 yd 16 yd13 yd

8-1 Estimating Perimeter and Area

8-1 Estimating Perimeter and Area-answers about 19 cm 2 about 7 cm 2 about 10 cm 2 about 18 cm 2 ft inmi 2

8-2 Area of a Parallelogram  height of a parallelogram – length of a perpendicular segment connecting base of parallelogram to the other.  Area of parallelogram: Area = bh

8-2 Area of a Parallelogram

8-2 Area of a Parallelogram-answers 60 m 2 25 m 2 12 ft in m 2

8-2 Area of a Parallelogram

8-2 Area of a Parallelogram-answers 3ft by 7 ft

8-3 Perimeter and Area of a Triangle  base of a triangle – any side can be considered base  height of triangle – length of perpendicular segment from a vertex to the bases opposite or and extension of base Area of triangle = ½ bh or bh/2

8-3 Perimeter and Area of a Triangle

8-3 Perimeter and Area of a Triangle - answers 8.2 ft 23.9 in 34.6 in 416 ft

8-3 Perimeter and Area of a Triangle

8-3 Perimeter and Area of a Triangle-ans 299 cm mi km yd 2 4, 4, 4; 5, 5, 2

8-4 Area of Other Figures  bases of trapezoid – two parallel sides of a trapezoid; b 1 and b 2  height of trapezoid – length of perpendicular segment connecting bases Area of trapezoid = ½h(b 1 + b 2 ) or h(b 1 + b 2 ) 2

8-4 Area of Other Figures

8-4 Area of Other Figures-answers 33 ft ft in 2 98 m km yd 2

8-5 Circumference and Area of a Circle Circumference – is the distance around the outside of a circle Π – the ratio of a circle’s circumference to its diameter d. Π is nonterminating and nonrepeating Π is approximate 3.14 or 22/7

8-5 Circumference and Area of a Circle

8-5 Circumference and Area of a Circle-answers C = Πd = Π*50 = cm C = 2 Πr = 2*Π*40 = in

8-5 Circumference and Area of a Circle

8-5 Circumference and Area of a Circle-answers C = Πd = Π*17 = 53.4 mm C = 2 Πr = 2*Π*7 = 44.0 cm

8-5 Circumference and Area of a Circle

A = Πr 2 = Π*6 2 = 36 Π = 113 in 2 A = Πr 2 = Π*15 2 = 225 Π = 707 ft 2

8-5 Circumference and Area of a Circle A = Πr 2 = Π*11 2 = 121 Π = 380 cm 2 A = Πr 2 = Π*25 2 = 625 Π = 1963 cm 2

8-8 Three-Dimensional Figures  3-D figure – figure that does not lie in plane  face – flat surface of solid shaped like polygon  edge – segment formed by intersection of 2 faces  prism – 3-D figure with two parallel and congruent polygonal faces, called bases

8-8 Three-Dimensional Figures Prisms are named for the shape of its bases. Name this prism.

8-8 Three-Dimensional Figures Cube - rectangular prism with faces that are all squares Cylinder - bases are circles

8-8 Three-Dimensional Figures Pyramids – are made up of triangular faces that meet at one point, called a vertex Cone – one base that is a circle and one vertex

8-8 Three-Dimensional Figures Sphere – set of all points in space that are same distance from a center point

8-8 Three-Dimensional Figures Sphere – set of all points in space that are same distance from a center point Rectangle, rectangular prism triangle, Triangular prism pentagon, Pentagonal prism

8-8 Three-Dimensional Figures

cylinder cone sphere Hexagonal pyramid cone Rectangular pyramid

8-9 Surface Area of Rectangular Prisms Net – two – dimensional pattern that you can fold into a 3-d figure

8-9 Surface Area of Rectangular Prisms Net – two – dimensional pattern that you can fold into a 3-d figure Draw a net for the triangular prism. 1)First label the bases and the side. 2)Then draw the net.

8-9 Surface Area of Rectangular Prisms-answers Net – two – dimensional pattern that you can fold into a 3-d figure

8-9 Surface Area of Rectangular Prisms Surface Area – sum of all the area of the faces of a prism

8-9 Surface Area of Rectangular Prisms-answers Surface Area – sum of all the area of the faces of a prism SA = ( )6 + (2*5*4) = = 148 in 2 TOP = 5*4 = 20 Bottom = 5 * 4 = 20 Left = 6 * 5 = 30 Right = 6 * 5 = 30 Front = 6 *4 = 24 Back = 6 * 4 = in 2

8-9 Surface Area of Rectangular Prisms Surface Area – sum of all the area of the faces of a prism

8-9 Surface Area of Rectangular Prisms Surface Area – sum of all the area of the faces of a prism SA = Ph + 2B = ( )6 + (2*7*4) = = 188 m 2 TOP = 7*4 = 28 Bottom = 7 * 4 = 28 Left = 6 * 4 = 24 Right = 6 * 4 = 24 Front = 6 *7 = 42 Back = 6 * 7 = m 2

8-9 Surface Area of Rectangular Prisms Surface Area – sum of all the area of the faces of a prism

8-9 Surface Area of Rectangular Prisms-ans Surface Area – sum of all the area of the faces of a prism SA = Ph + 2B = ( )2 + (2*1*1) = = 10 ft 2 TOP = 1*1 = 1 Bottom = 1* 1 = 1 Left = 1 * 2 = 2 Right = 1 * 2 = 2 Front = 1 *2 = 2 Back = 1 * 2 = ft 2

8-9 Surface Area of Triangular Prisms Surface Area – sum of all the area of the faces of a prism

8-9 Surface Area of Triangular Prisms-ans Surface Area – sum of all the area of the faces of a prism SA = Ph + 2B = ( )4 + 2((9*12)/2) = = 252 cm 2 TOP (triangle) = 9 * 12 / 2 = 54 Bottom (triangle) = 9 * 12 / 2 = 54 Left (rectangle) = 9*4 = 36 Front (rectangle) = 15*4 = 60 Back (rectangle) = 12 * 4 = cm 2

8-9 Surface Area of Triangular Prisms Surface Area – sum of all the area of the faces of a prism

8-9 Surface Area of Triangular Prisms-ans Surface Area – sum of all the area of the faces of a prism SA = Ph + 2B =(6+8+10)9 + 2((6*8)/2) = = 264 m 2 Left (triangle) = 6 * 8 / 2 = 24 Right (triangle) = 6 * 8 / 2 = 24 Front (rectangle) = 9*10 = 90 Back (rectangle) = 9*6 = 54 Bottom (rectangle) = 8*9 = m 2

8-9 Surface Area of Cylinders Surface Area – sum of all the area of the faces of a prism

8-9 Surface Area of Cylinders Surface Area – sum of all the area of the faces of a prism

8-9 Surface Area of Cylinders-ans Surface Area – sum of all the area of the faces of a prism SA = 2 Πrh + 2Πr 2 = 2 Π10*15 + 2Π10 2 = = 1570 yd 2

8-9 Surface Area of Cylinders Surface Area – sum of all the area of the faces of a prism

8-9 Surface Area of Cylinders-ans Surface Area – sum of all the area of the faces of a prism SA = 2 Πrh + 2Πr 2 = 2 Π5*20 + 2Π5 2 = = 785 cm 2

8-9 Surface Area of Cylinders Surface Area – sum of all the area of the faces of a prism

8-9 Surface Area of Cylinders-ans Surface Area – sum of all the area of the faces of a prism SA = 2 Πrh + 2Πr 2 = 2 Π10*45 + 2Π10 2 = = 3454 m 2

8-10 Volume of Prisms and Cylinders Volume – number of cubic units needed to fill the space INSIDE the figure Cubic unit – a cube with edges one unit long

8-10 Volume of Prisms and Cylinders

Volume of a Rectangular Prism V = Bh = area of base * height = l * w * h

8-10 Volume of Prisms and Cylinders

8-10 Volume of Prisms and Cylinders-answers V = Bh = l * w * h = 20 * 7 * 8 = 1120 in 3 V = Bh = l * w * h = 8 * 10 * 8 = 640 ft 3

8-10 Volume of Prisms and Cylinders

8-10 Volume of Prisms and Cylinders-ans V = Bh = b*h * h 2 = 6*6* 8 2 = 192 cm 3 V = Bh = b*h * h 2 = 3*4* 5 2 = 30 in 3

8-10 Volume of Prisms and Cylinders

8-10 Volume of Prisms and Cylinders-ans V = Bh = b*h * h 2 = 12*28* 10 2 = 1680 m 3

8-10 Volume of Prisms and Cylinders Find the height of each rectangular prism given the volume, length, and width. V = 3375 m 3 V = 900 ft 3 L = 15 m L= 45 ft W = 15 m W = 2 ft H = ?

8-10 Volume of Prisms and Cylinders-ans Find the height of each rectangular prism given the volume, length, and width. V = 3375 m 3 V = 900 ft 3 L = 15 m L= 45 ft W = 15 m W = 2 ft H = ? 15 m H = ? 10 ft

8-10 Volume of Prisms and Cylinders

8-10 Volume of Prisms and Cylinders-ans V = Bh = Πr 2 * h = Π 1 2 * 10 = 31 ft 3 V = Bh = Πr 2 * h = Π 14 2 * 80 = m 3

8-10 Volume of Prisms and Cylinders

8-10 Volume of Prisms and Cylinders-ans V = Bh = Πr 2 * h = Π 6 2 * 18 = 2036 in 3