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Comprehensive Guide to Geometry: Areas, Surfaces, and Volumes

Learn how to calculate areas of shapes, find the surface areas of solids like prisms and cylinders, and determine volumes of cubes, pyramids, and cones. Explore key formulas and examples in geometry concepts.

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Comprehensive Guide to Geometry: Areas, Surfaces, and Volumes

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  1. JournalChapter 9 – 10 José Pablo Reyes10 – 5

  2. Describe how to find the areas of a square, rectangle, triangle, parallelogram. Square: multiplythe base times itsself Rectangle: multiplythe base times theheight (bxh) Triangle: multiplythe base times theheight time half (bxhx1/2) Parallelogram: multiplythe base times theheight (bxh)

  3. Examples

  4. Describe how to find the areas of a trapezoid, kite and rhombus. Trapezoid: addthelenght of twoparallelsides, then divide by 2 and multiplythisbytheheight Kite: A=1/2xy Rhombus: ½(diagonal 2)(diagonal 1)

  5. Describe how to find the area of a composite figure. Explain what a composite figure is. Composite figure: any figure/shapethat can bedividedinto more thanonebasic figure. A figure thatismadefromtwoor more geometric figures Area of a composite figure: A=A1+A2

  6. Examples

  7. Describe how to find the area of a circle. Area of a Circle: A=π(r²) Examples:

  8. Describe what a solid is. A solidis a three dimensional figure, it can me bemade up of flat or curve surfaces. Face: any flat surface in the figure Edge: segmentthatistheintersection of two faces Vertex: point of intersection of 3 or more faces

  9. Examples

  10. Describe how to find the surface area of a prism. What is a prism? Explain what a “Net” is. Prism: 3D figure formedbytwoparallelcongruentpolygonal faces called bases, which are connectedby faces that are parallelograms Net: a diagram of thesurfaces of a 3D figure that can befoldedtoformthe figure. A=2LW + 2(L+W)H

  11. Examples

  12. Describe how to find the surface area of a cylinder. Tofindthesurfacearea of a cylinder do de following; surfacearea of a cylinder = 2π(r2) + 2π(r)(h). Examples

  13. Describe how to find the surface area of a pyramid. What is a pyramid? Pyramid: 3D figure formedby a polygonal base and triangular faces thatmeet at a commonvertex Tofindthesurfacearea of a pyramid do thefollowing; findthe base areawith b², once youknowthe base area and all faces are thesame, do this: Base area + ½ x Perimeter x Slantlenght, ifthe faces are notthesame do this, Base Area + lateral area Lateral area = allsidesthat are notthe base Slantlenght = lenght of thesegment, fromthemidpoint of the base to a vertex

  14. Describe how to find the surface area of a cone Tofindthesurfacearea of a cone; findthearea of thecircle, thenturntheshapeintoits net. Addthemeasures up and thatsthearea of thecone.

  15. Describe how to find the volume of a cube Tofindthesurfacearea of a cube do thefollowing; findthesurfacearea of oneside and multiplyitby 6. SA= 6(a²)

  16. Examples

  17. Describe Cavalieri’sprinciple. Iftwo 3D figures havethesame base are and sameheight, thentheywillhavethesamevolume Examples

  18. Describe how to find the volume of a prism and a cylinder. Prism: area of base X height Rectangular prism: L x W x H Cylinder: π(r²)addthearea of the 2 faces, findthearea of the bases usingthe formula A=π(r2), the combined surface area of the faces is 2π(r2). Then find the surface area of the side which is circumference X height or 2π(r)(h).

  19. Examples

  20. Describe how to find the volume of a pyramid and a cone. Tofindthevolume of a pyramid use thefollowing formula; 1/3 b(h) Tofindthevolume of a cone use thefollowing formula; 1/3 x π(r²)h

  21. Examples

  22. Describe how to find the surface area and volume of a sphere Tofindthesurfacearea of a sphereyouhaveto use this formula; 4π(r²) To find the volume of a sphere use this formula; 4/3 π(r³)

  23. Examples

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