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Rodrigo Maselli Journal 9 and 10

Rodrigo Maselli Journal 9 and 10. areas of a square, rectangle, triangle, parallelogram, trapezoid, kite and rhombus:. Formulas for area. Examples. Composite figures. A composite figure is a shape made up of more than one figure.

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Rodrigo Maselli Journal 9 and 10

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  1. Rodrigo Maselli Journal 9 and 10

  2. areas of a square, rectangle, triangle, parallelogram, trapezoid, kite and rhombus:

  3. Formulas forarea

  4. Examples

  5. Composite figures • A composite figure is a shape made up of more than one figure. • To find the area of such figure, you need to break it down into pieces and find the area of the broken down shapes. • After this, you need to add the areas you have found.

  6. Examples

  7. Area of a circle • The formula for the area of a circle isπr2. • Or π(d/2)2 • Pi is an irrational number most of the time stated as 3.14

  8. Examples

  9. Solids • A solid is any three dimensional figure (Height width and depth) • It has sides, edges, faces and corners. • Its perimeter is called surface area and its area is called volume.

  10. Examples

  11. Prisms • A prism is a three dimensional shape with two of its bases being congruent figures. • This congruent shapes are connected by parallel lines • The surface area of a prism is the twice the base area of one of the congruent bases plus the lateral area (Length times width of the sides) • A net is a diagram of all of the faces of a prism on the same plane.

  12. Examples

  13. Cylinder • A cylinder is made up of two circles connected by a round surface. • To find its surface area you find the area of both of the circles and then of the lateral surface. • The formula to find the surface area of a cylinder is 2 πr 2 + 2πrh

  14. Examples

  15. Pyramids • A pyramid is formed by a shape as a base and triangular faces that meet at a common end point at the top. • To find its surface area, you have to first find the area of the base, then find the area of the sides which are all triangles and add them all up. • The formula to find the surface area of such is: L+B

  16. Examples

  17. Cones • A cone is a three dimensional figure formed by a circular base with its lateral face being curved and ending at a common vertex. • To find its surface area you have to find the area of the circle base and then add the lateral surface area • The lateral surface area is found by multiplying the slant height squared by pi.

  18. Examples

  19. Cube • To find the volume of a cube you multiply length times width time the height of the cube. • The formula is L3

  20. Examples

  21. Cavalieri’s principle • Cavalieri’s principle states that if on two three dimensional shapes the surface area of the base is the same and the cross sectional area is the same (this including the same height) then the two shapes have the same volume.

  22. Examples Assuming they both have the same surface area and exactly the same cross sectional area they have the same volume (drawing not to scale)

  23. Volume of a prism • The volume of a prism is simple, it’s the area of the base times its height. • The formula is V= BH

  24. Exampels

  25. Volume of a Cylinder • The volume of a cylinder is also quite simple, you find the area of the base times its height also. • The area of the base is the area of the circle at the bottom.

  26. Examples

  27. Volume of a pyramid • The volume of a pyramid is the same as both past ones just that this one is divided by three. • It is the area of the base, times the height and all of it divided by three (or multiplied by one third)

  28. Examples

  29. Volume of a Cone • The volume of a cone is the same of that of a pyramid only that the cone has a circular base. • So the volume is found by multiplying the area of the base, times the height divided by three (Or multiplied by one third)

  30. Examples

  31. Sphere • The surface area of a sphere is found by multiplying four by pi squared. • The formula is 4πr2

  32. Examples

  33. Volume of a sphere • The volume of the sphere is simple, you have to multiply four thirds by three, and then by pi cubed. • The formula is 4/3πr3

  34. Examples

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