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Notes: Geometry (6.G.1-4) Notes: Geometry (6.G.1­4) Perimeter ­ Add up all the sides (P =s + s + s...) Perimeter ­ The distance around a polygon. Square A = side2 A = S2 s Examples: Rectangle A = Length x Width A = lw 14 cm 8 m L 7 m w 3 cm 8 m Parallelogram A = Base x Height A = bh b 20 m h o b *Height is found at the 90 angle. P = ____________14 + 3 + 14 + 3 P = ____________8 + 8 + 20 Triangle A = Base x Height A = bh 2 2 P = _______34 cm P = _______36 m h h 1 o A = /2bh b b *Height is found at the 90 angle. Formulas ­ Perimeter and Area Perimeter 5 Perimeter ­ The distance around a polygon. Perimeter ­ The distance around a polygon. Examples: 10 in Examples: 6 ft I I I 9cm 24cm 3 in 9 in I I I I 11cm I 16 in I 4cm 17cm 3x + 2 P = ____________6 + 6 + 6 + 6 P = ____________16+9+10+6+6+3 P = ____________5(3x + 2) P = ____________9 + 17 + 24 P = _______24 ft P = _______50 in P = _______15x + 10 P = _______50 cm Perimeter Perimeter Area ­ The number of square units it takes to Area ­ The number of square units it takes to cover the figure. (The size of the figure.) cover the figure. (The size of the figure.) Examples: Examples: 14 cm 9yd 8 m 7 m 4yd 8 m 18 m 3 cm 8 m 5yd 6 m 20 m 1yd 2 m 11 m A = ____________Length x Width A = ____________Base x Height 2 A = ____________Base x Height A = ____________Base x Height 2 A = ____________14 x 3 A = ____________20 x 7 2 A = ____________9 x 4 A = ____________11 x 6 2 A = ____________42 cm2 A = ____________70 m2 A = ____________36 yd2 A = ____________33 m2 Area Area 1 Notes: Geometry (6.G.1­4) How to solve area problems backwards? Examples: A = 70 m2 A = 42 yd2 Steps: 7 yd (1) Write the Formula. 14 m Find the length. Find the height. (2) Plug in all information you know. A = L x W A = b x h 2 (3) Solve for unknown information. 42 = L x 7 70 =14 x h 2 (4) Make sure you answered what the question 7 7 70 = 7h is asking. 6 = L 7 7 (5) Write units on your answer. 10 = h 6 yd 10 m Working Area Backwards Working Area Backwards Volume ­ The number of cubic units needed to Volume ­ The number of cubic units needed to fill a given space. fill a given space. Volume of a Rectangular Prism Volume of a Rectangular Prism V = L W H 1 V = L W H 3 cm 1 /2 m 1 3 1 V = 20 8 3 V = 14 /2 2 /4 1 /2 3 1 13 3 20 cm V = 480 cm 14 /2 m V = 59 /16 m 3 8 cm 2 /4 m *Units are always cubed* *Units are always cubed* Finding Volume Finding Volume with Fractions 1 A right rectangular prims has edges of 1 /4 ft, 1 A right rectangular prims has edges of 1 /4 ft, 1 1 ft, and 1 /2 ft. How many cubes with a side 1 1 ft, and 1 /2 ft. How many cubes with a side 1 length of /4 ft would be needed to fill the prism? 1 length of /4 ft would be needed to fill the prism? 1 Step #1 Volume of Prism 1 /2 ft 1 1 /2 ft 1 V = L x W x H 1 /4 ft Steps: 1 1 1 1 /4 ft V = 1 /2 x 1 x 1 /4 1 ft Find the Volume of the prism. 7 3 1 ft V = 1 /8 ft Step #3 Find the Volume of the cube going into the prism. 7 1 Step #2 Volume of the Cube 1 /8 /64 = Divide the Prism Volume by the Volume of the cube 15 1 = V = L x W x H 8 64 going into it. This will tell you how many cubes it takes 1 1 1 K C F to fill the prism. V = /4 x /4 x /4 15 64= 120 *See work to the right* V = 1/ ft3 8 1 64 120 cubes Finding out How Many Cubes Fit into a Prism Finding out How Many Cubes Fit into a Prism 2 Notes: Geometry (6.G.1­4) 6.G.4 Nets and Surface Area Review: I can...identify the different types of ________ nets • To find the area of a rectangle: that go with different 3­dimensional figures. I can ...find the _____________ of different 3 surface area Area = ________________Length x Width dimensional figures. _________is a two­dimensional representation A net • To find the area of a triangle: of a three­dimensional figure. Surface Area (S.A.) is the _____________ that total area 1/ (Base x Height) covers a 3 dimensional figure. Area = ____________ or _______________Base x Height 2 2 A Polyhedron is a 3­D solid with __________flat faces Nets and Surface Area Formulas Review A Prism: Vertex: Vertices is the plural • is a ____________________polyhedron form of vertex. It is where the • it is a 3­dimensional shape with 2 ________, identical edges of a 3­D figure meet. parallel bases. • all other faces are ______________ rectangles Face: a flat surface of • a prism takes its name from the shape of its a 3­D figure. _______bases Edges: The side of a polygon where two faces of a solid figure meet. Triangle Rectangle Pentagon Octagon Prisms Parts of a #­D Figure Square Prisms (cubes) have Nets of a _________________Square Prism (Cube) • 6 square faces all of ______ size.equal • 8 _________vertices • 12 ______ edgesequal Square Prism Square Prism Net 3 Notes: Geometry (6.G.1­4) Rectangular Prisms have Net of a ___________________Rectangular Prism • 6 faces that are ___________rectangles • Opposite faces are parallel and ________congruent • 8 vertices • 12 edges Rectangular Prism Rectangular Prism Net Triangular Prisms have Nets of a __________________Triangular Prism • 2 identical triangular bases, they are congruent and _____________parallel • 2 bases (triangles) and 3 faces (rectangles) • 9 ___________edges • 6 ___________vertices Triangular Prism Triangular Prism Net Pyramid: Slant height is the height of each __________.lateral face • is a polyhedron. • a solid shape (3­D shape ) with a _________ polygon as its base. • has __________faces that taper into one triangular point (vertex). • A pyramid takes the name of the shape of its h h ________.base Triangular Rectangular Triangle Rectangle Pentagon Octagon Pyramid Pyramid Pyramid Slant Heights on Pyramids 4 Notes: Geometry (6.G.1­4) Net of a ___________________Square Pyramid Net of a ___________________Rectangular Pyramid I I I I Square Pyramid Net Rectangular Pyramid Net Net of a ___________________Triangular Pyramid Prism Both Pyramid Congruent Takes the name Tapers to a Faces of its base point Parallel Bases 3­Dimensional Has lateral faces Has triangular faces Triangular Pyramid Net Compare and Contract of Prisms and Pyramids Find the surface area of the cube. Find the surface area of the rectangular prism. 3" 5 cm 5" 5" 3" 3" 5" 5 cm 8" Add these 8" Numbers 2 What is the AREA of one face?_______25cm Top and Bottom 2 x 8 x 3 48 How many faces does the cube have?______6 2 x l x w Two side areas Multiply the area of one face by the total 2 x h x w 2 x 5 x 3 30 number of faces. __________25 x 6 Front & Back 2 x 8 x 5 2 x l x h 80 Total Surface area:_________150cm2 Total Surface Area:____________158 square inches Surface Area of a Cube Surface Area of a Rectangular Prism 5 Notes: Geometry (6.G.1­4) Find the area of the triangular prism. Find the area of the square pyramid. 3 cm. 10m 8m Add these 6 cm. 10m numbers 15m Add these 6 x 6 36 10m Numbers Square (l x w) Triangle #1 Triangles 1 1/ x 10 x 8 x 2 80 /2 x 6 x 3 9 ½bh x2 2 (1/2 x b x h) Rectangle #1 Triangle #2 1 l x w 10 x 15 150 (1/2 x b x h) /2 x 6 x 3 9 Rectangle #2 Triangle #3 10 x 15 150 1 l x w (1/2 x b x h) /2 x 6 x 3 9 Rectangle #3 10 x 15 150 Triangle #4 1/ x 6 x 3 9 l x w (1/2 x b x h) 2 Total Surface Area:___________________530 meters squared Surface Area:_______72 cm2 Surface Area of a Triangular Prism Surface Area of a Square Pyramid Find the area of the rectangular pyramid. 12 m Find the surface area of a triangular pyramid (base is an equilateral triangle) 8 m 6m Triangle #1 1 Rectangle(l x w) 8 x 6 48 14 m /2 x 6 x 10 30 (1/2 x b x h) 10 cm Triangle #1 Triangle #2 1 1 (1/2 x b x h) /2 x 8 x 12 48 (1/2 x b x h) /2 x 6 x 10 30 Triangle #2 Triangle #3 6 cm 1 1 (1/2 x b x h) /2 x 8 x 12 48 (1/2 x b x h) /2 x 6 x 10 30 Triangle #3 Triangle #4 1/ x 6 x 14 42 1 (1/2 x b x h) 2 (1/2 x b x h) /2 x 6 x 10 30 Triangle #4 1/ x 6 x 14 42 (1/2 x b x h) 2 Surface Area:________120 cm2 Surface Area:_______228 m2 Surface Area of a Rectangular Pyramid Surface Area of a Triangular Pyramid 6.
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