Notes: Geometry (6.G.1 4)

Transcription

1 Perimeter Add up all the sides (P =s + s + s...) Square A = side 2 A = S 2 Perimeter The distance around a polygon. Rectangle w s L A = Length x Width A = lw Parallelogram A = Base x Height A = h h Triangle A = Base x Height A = h 2 2 h h A = 1 / 2 h *Height is found at the 90 o angle. *Height is found at the 90 o angle. 14 cm P = P = 34 cm 7 m 20 m P = P = 36 m Formulas Perimeter and Area Perimeter Perimeter The distance around a polygon. 5 Perimeter The distance around a polygon. 10 in 6 ft P = in 16 in 3 in P = x + 2 P = 5(3x + 2) 11cm 9cm 4cm 24cm 17cm P = P = 24 ft P = 50 in P = 15x + 10 P = 50 cm Perimeter Perimeter Area The numer of square units it takes to cover the figure. (The size of the figure.) 14 cm 7 m 20 m A = Length x Width A = Base x Height 2 A = 14 x 3 A = 20 x 7 2 A = 42 cm 2 A = 70 m 2 Area The numer of square units it takes to cover the figure. (The size of the figure.) 5yd 9yd 4yd 6 m 1yd 2 m 11 m A = Base x Height A = Base x Height 2 A = 9 x 4 A = 11 x 6 2 A = 36 yd 2 A = 33 m 2 1 Area Area 1

2 How to solve area prolems ackwards? Steps: (1) Write the Formula. (2) Plug in all information you know. (3) Solve for unknown information. (4) Make sure you answered what the question is asking. (5) Write units on your answer. A = 42 yd 2 Find the length. A = L x W 42 = L x = L 6 yd 7 yd A = 70 m 2 14 m Find the height. A = x h 2 70 =14 x h 2 70 = 7h = h 10 m Working Area Backwards Working Area Backwards Volume The numer of cuic units needed to fill a given space. Volume The numer of cuic units needed to fill a given space. Volume of a Rectangular Prism Volume of a Rectangular Prism V = L W H V = / 2 m V = L W H V = 14 1 / / / 2 20 cm V = 480 cm / 2 m V = / 16 m 3 8 cm *Units are always cued* 2 3 / 4 m *Units are always cued* Finding Volume Finding Volume with Fractions A right rectangular prims has edges of 1 1 / 4 ft, 1 ft, and 1 1 / 2 ft. How many cues with a side length of 1 / 4 ft would e needed to fill the prism? Steps: Find the Volume of the prism. 1 ft 1 1 / 2 ft 1 1 / 4 ft Find the Volume of the cue going into the prism. Divide the Prism Volume y the Volume of the cue going into it. This will tell you how many cues it takes to fill the prism. *See work to the right* A right rectangular prims has edges of 1 1 / 4 ft, 1 ft, and 1 1 / 2 ft. How many cues with a side length of 1 / 4 ft would e needed to fill the prism? Step #1 Volume of Prism V = L x W x H V = 1 1 / 2 x 1 x 1 1 / 4 V = 1 7 / 8 ft 3 Step #2 Volume of the Cue V = L x W x H V = 1 / 4 x 1 / 4 x 1 / 4 V = 1 / 64 ft 3 1 ft 1 1 / 2 ft Step #3 1 1 / 4 ft 1 7 / 8 1/ 64 = 15 1 = 8 64 K C F = cues Finding out How Many Cues Fit into a Prism Finding out How Many Cues Fit into a Prism 2

3 6.G.4 Nets and Surface Area can...identify the different types of nets that go with different 3 dimensional figures. can...find the surface area of different 3 dimensional figures. is A net a two dimensional representation of a three dimensional figure. Surface Area (S.A.) is the total area that covers a 3 dimensional figure. A Polyhedron is a 3 D solid with flat faces Review: To find the area of a rectangle: Area = Length x Width To find the area of a triangle: Area = Base x Height or 1/ 2 (Base x Height) 2 Nets and Surface Area Formulas Review A Prism: is a polyhedron it is a 3 dimensional shape with 2, identical parallel ases. all other faces are rectangles a prism takes its name from the shape of its ases Vertex: Vertices is the plural form of vertex. t is where the edges of a 3 D figure meet. Face: a flat surface of a 3 D figure. 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 (cues) have Nets of a Square Prism (Cue) 6 square faces all of equal size. 8 vertices 12 equal edges Square Prism Square Prism Net 3

4 Rectangular Prisms have 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 ases, they are congruent and parallel 2 ases (triangles) and 3 faces (rectangles) 9 edges 6 vertices Triangular Prism Triangular Prism Net Pyramid: is a polyhedron. a solid shape (3 D shape ) with a polygon as its ase. has faces triangular that taper into one point (vertex). A pyramid takes the name of the shape of its. ase Slant height is the height of each. lateral face h h Triangle Rectangle Pentagon Octagon Triangular Pyramid Rectangular Pyramid Pyramid Slant Heights on Pyramids 4

5 Square Pyramid Rectangular Pyramid Square Pyramid Net Rectangular Pyramid Net Triangular Pyramid Prism Both Pyramid Congruent Faces Takes the name of its ase Tapers to a point Parallel Bases 3 Dimensional Has lateral faces Has triangular faces Triangular Pyramid Net Compare and Contract of Prisms and Pyramids Find the surface area of the cue. 5 cm 5 cm What is the AREA of one face? 25cm 2 How many faces does the cue have? 6 Multiply the area of one face y the total numer of faces. 25 x 6 Total Surface area: 150cm 2 Find the surface area of the rectangular prism. 8" 3" 5" 3" 5" 8" 3" 5" Add these Numers Top and Bottom 2 x l x w Two side areas 2 x h x w Front & Back 2 x l x h 2 x 8 x 3 2 x 5 x 3 2 x 8 x Total Surface Area: 158 square inches Surface Area of a Cue Surface Area of a Rectangular Prism 5

6 Find the area of the triangular prism. 8m 10m 10m 10m 15m Add these Numers Triangles ½h x2 Rectangle #1 l x w Rectangle #2 l x w Rectangle #3 l x w 1/ 2 x 10 x 8 x 2 10 x x x Total Surface Area: 530 meters squared Find the area of the square pyramid. Square (l x w) Triangle #1 Triangle #2 Triangle #3 Triangle #4 Add these numers 6 x cm. Surface Area: 72 cm 2 Surface Area of a Triangular Prism Surface Area of a Square Pyramid Find the area of the rectangular pyramid. Rectangle(l x w) Triangle #1 Triangle #2 Triangle #3 Triangle #4 8 x / 2 x 8 x / 2 x 8 x / 2 x 6 x m 6m 14 m 1/ 2 x 6 x Surface Area: 22 2 Find the surface area of a triangular pyramid (ase is an equilateral triangle) Triangle #1 Triangle #2 Triangle #3 Triangle #4 Surface Area: 120 cm 2 10 cm 6 cm Surface Area of a Rectangular Pyramid Surface Area of a Triangular Pyramid 6