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POLYHEDRAL

POLYHEDRAL. For Grade VIII/ Semester 2. Written by:. Ririn Aprianita, S.Pd.Si. Standard of Competence. Understanding the properties of cube, cuboid, prism, pyramid, and their parts, and determining the measurements. Basic Competency.

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POLYHEDRAL

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  1. POLYHEDRAL For Grade VIII/ Semester 2 Written by: Ririn Aprianita, S.Pd.Si

  2. Standard of Competence Understanding the properties of cube, cuboid, prism, pyramid, and their parts, and determining the measurements.

  3. Basic Competency Identifying the properties of cube, cuboid, prism, pyramid, and their parts

  4. Have you ever seen the objects below? Let’s learn about them

  5. CUBE CUBE is enclosed by 6 planes which are the CONGRUENT SQUARES. The intersecting planes are perpendicular to each other.

  6. CUBE G H E F face D C B A edge vertex How many vertices does the cube have? 8 They are vertex A, B, C, D, E, F, G How many edges does the cube have? 12 They are edge AB, BC, CD, AD, …,…,…,…,…,…,…,… How many faces does the cube have? 6 They are face ABCD, EFGH, ADHE, …,…,…

  7. CUBE BG is called face diagonal (=diagonal sisi). Find the other face diagonals! H G From one vertex, how many face diagonals we can make? E F How many face diagonals does the cube have? D C Are they congruent? A B If the length of its edge is s, what is the length of its face diagonals?

  8. CUBE AG is called space diagonal (=diagonal ruang). Find the other space diagonals! H G From one vertex, how many space diagonals we can make? E F How many space diagonals does the cube have? D C Are they congruent? A B If the length of its edge is s, what is the length of its space diagonals?

  9. CUBE ABGH is called diagonal plane (=bidang diagonal). H G What is the shape of diagonal plane? E F Can you find the other diagonal planes? D C How many diagonal planes does the cube have? A B Are they congruent?

  10. CUBE Dimension of diagonal plane: G H H G E F face diagonal D C A B A B edge If the length of edge is ‘s’, what is the area of diagonal plane?

  11. CUBOID W V T U S R P Q Cuboid is enclosed by 6 planes, which its base and top are rectangular shaped. The intersecting planes are perpendicular to each other.

  12. CUBOID W V T U face S R P Q edge vertex How many vertices, edges, and faces does the cube have?

  13. CUBOID W V T U S R P Q The dimension of cuboid Length PQ, …, …, … Width TW, …, …, … Height VR, …, …, …

  14. CUBOID W V How many face diagonals does cuboid have? U T S R Are they congruent? P Q Let the length, width, and height are l, w, and h, respectively. What is the measurement of its face diagonals?

  15. CUBOID W V How many space diagonals does cuboid have? U T S R Are they congruent? P Q Let the length, width, and height are l, w, and h, respectively. What is the measurement of its space diagonal?

  16. CUBOID W V How many diagonal plane does cuboid have? U T S R Are they congruent? P Q What is the shape of cuboid’s diagonal plane? Sketch all possible diagonal plane, determine its measurement, and calculate the area of them.

  17. PRISM top F lateral face E D C A B base

  18. PRISM A prism is a three dimensional shape that constructed of TWO PARALLEL AND CONGRUENT POLYGONS and the other faces are RECTANGLES or PARALLELOGRAMS. F E D F C D E A B C A Oblique prism B Right prism

  19. PRISM Regular triangular prism Triangular prism Rectangular prism Pentagonal (5-sided) prism Hexagonal (6-sided) prism

  20. PRISM Fill the table below, by investigating in your group discussion.

  21. PRISM For n-sided based prism, we can conclude that: 2n The number of its vertices is The number of its edges is 3n The number of its faces is n + 2 The number of its face diagonal is n2 – n The number of its space diagonal is n2 – 3n The number of its diagonal plane is (n2– n)/2; if n is even number or (n2– 3n)/2; if n is odd number

  22. PYRAMID top lateral face base Pyramid is a polyhedral which enclosed by A POLYGON AS ITS BASE and TRIANGLES AS ITS LATERAL FACES.

  23. PYRAMID There are many kinds of pyramid, based on the shape of its base. T P E C T A D B A Triangular pyramid B S C R Pentagonal pyramid P Q Rectangular pyramid

  24. PYRAMID Fill the table below, by investigating in your group discussion.

  25. PYRAMID For n-sided based pyramid, we can conclude that: n + 1 The number of its vertices is The number of its edges is 2n The number of its faces is n + 1 The number of its diagonal plane is (n2– 3n)/2 Triangular shaped

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