2. MATHEMATICS Welcome To

3. R.R.Rozindar (Maths teacher) Govt High School Hanjagi, Tq: Indi Dist: Bijapur.

4. Polyhedra Class X

5. OBJECTIVES After learning this chapter you will be able to Define polygon, regular polygon and polyhedra. Identify different types of polyhedron. Name different types of platonic solids. Find the number of faces, vertices and edges of given polyhedron. Verify EULER’s formula.

6. Introduction You may come across many solids of different shapes such as Sweet Box Cubical Eraser Gift BoxSolar Cooker Instrument Box Box Triangular prism Prisms

7. Introduction What is the shape of each face of the objects you have seen ? Ans : Triangle, Rectangle. Ans : Triangle, Rectangle. What these shapes usually called as ? Ans : Polygons. Ans : Polygons.

8. Polyhedra Definition of Polygon Regular polygon Polyhedron polyhedral solid Regular polyhedra

9. Polygon A closed figure bounded by straight line segments. The region bounded by polygon is polygonal region. This is a Polygonal Region

10. Regular Polygon It is a polygon having equal sides and equal angles. Equilateral Triangle Square

11. Polyhedron A closed figure in the space bounded by polygonal faces is a polyhedron. A polyhedron divides the space in two regions, within the polyhedron and outside it. Inner Region Of Polyhedron

12. Polyhedral solids A polyhedron has Edges, Vertices and Faces Edges = 12 All sides are equal Vertices = 8 Faces = 1432 5 6 6

13. Regular Polyhedra A polyhedron is called a regular polyhedron, if its faces are congruent regular polygons. There are only Five regular polyhedrons. Tetrahedron Hexahedron Octahedron Dodecahedron Icosahedron

14. Regular Polyhedra These polyhedra are known as PLATONIC SOLIDS It is believed that he associated these with Fire Earth Air Universe Water

15. Tetrahedron This polyhedron is called Tetrahedron because it has Four faces. 4 1 32 Faces = F = 4

16. Tetrahedron This polyhedron is called Tetrahedron because it has Four faces. Edges = E = 6 Faces = F = 4 All sides are equal

17. Tetrahedron This polyhedron is called Tetrahedron because it has Four faces. Faces = 4 Edges = 6 Vertices = V V = 4

18. Hexahedron This polyhedron is called hexahedron because it has six faces 1 65 4 3 2 Faces = F F = 6

19. Hexahedron This polyhedron is called hexahedron because it has six faces Faces =6 Edges = E E = 12 ++

20. Hexahedron This polyhedron is called hexahedron because it has six faces Faces = 6 Edges = 12 Vertices = V + V = V = 8

21. Octahedron This polyhedron is called Octahedron because it has Eight faces Faces = 8 2 3 4 8 516 7

22. Octahedron This polyhedron is called Octahedron because it has Eight faces Faces = 8 Edges = E E = 12 ++

23. Octahedron This polyhedron is called Octahedron because it has Eight faces Faces = 8 Edges = 12 + V = 6 Vertices = V

24. Dodecahedron This polyhedron is called Dodecahedron because it has twelve faces. Number of Faces = F 2 3 5 1 6 4 11 7 12 10 9 8 Faces = F = 12

25. Dodecahedron This polyhedron is called Dodecahedron because it has twelve faces. Number of Faces=F=12 +++++ Edges = E E = 30

26. Dodecahedron This polyhedron is called Dodecahedron because it has twelve faces. Number of Faces=F=12 Edges=E=30 ++ + Vertices = V V = 20

27. Icosahedron This polyhedron is called Icosahedron because it has Twenty faces 12 3 45 8 97 10 6 11 12 13 14 15 1617181920 Faces = F F = 20

28. Icosahedron This polyhedron is called Icosahedron because it has Twenty faces Faces = 20 Edges = E E = 30 = ++ ++ +

29. Icosahedron This polyhedron is called Icosahedron because it has Twenty faces Faces = 20 Edges = E Vertices = V++= V= 12

30. Euler’s Formula Sl. No Name of the polyhedron FacesVerticesEdges 1 Tetrahedron446 2 Hexahedron6812 3 Octahedron8612 4 Dodecahedron122030 5 Icosahedron201230F+VE+288 1414 1414 3232 3232 F + V = E + 2

31. Euler’s Formula Euler’s formula for polyhedra is,Euler’s formula for polyhedra is, F + V = E + 2F + V = E + 2 Leonard Euler (1707-1783)

32. Test Your self Regular polyhedra are also called as ……………… Shape of each face of tetrahedron is………………. Euler’s formula for polyhedron is …………….. Platonic solids. Equilateral Triangle F + V = E + 2.

33. Home Assignment Verify Euler’s formula for square based pyramid.

34. Recap Polygon:Polygon: -A closed figure bounded by straight line segments. Regular polygon:Regular polygon: - Polygon having equal sides and equal angles. Polyhedron:Polyhedron: - A closed figure in the space bounded by polygonal faces. Regular polyhedron:Regular polyhedron: - A polyhedron having congruent regular polygonal faces. Platonic Solids: Tetrahedron. Hexahedron. Octahedron. Dodecahedron. Icosahedron.

35. Know About. PLATOPLATO a Greek mathematician “ Let no one enter who is ignorant of geometry”.He founded the academy and over the entrance he inscribed, “ Let no one enter who is ignorant of geometry”.

36. Know About. University Entrance.

37. Know About. Ruins Of University