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# Geometry

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### Geometry

1. 1. Let’s Play withShapes…In Geometry!
2. 2. How do you find the area of a rectangle?l(length)w (width)The formula for Area of arectangle is A=l  w(Area=length  width)**For a square, all sides areequal. So the formula will be A=s  s = s2 (Area= side  side =side2 )ss
3. 3. How do you find the area of atriangle?The formula for Area of aTriangle is A= ½ b  h (Area= ½ base  height )Practice!In a triangle with base = 10 in, and height = 6 in, what isthe area?A = ½  (10 in)  (6 in) = 30 in2 The area is 30 in2 .
4. 4. How do you find the area of atrapazoid?The formula for the Area of aTrapazoid is A= ½  (b1 + b2 ) h ( Area= ½  ( base1 + base2 ) height )Practice!In a trapazoid with base1 = 5 m, base2 = 3 m, and height = 2 m, what isthe area?Area = ½ (5 m + 3 m)  2 m = ½  8 m  2 m = 8 m2The area is 8 m2 .
5. 5. How do you find the area of acircle?The formula for the Area of aCircle isA = π  r2 ( Area = π (pi)  radius2)*The radius is half of the diameter.*The number pi can be replaced by3.14 or 22/7 depending on what isspecified. Using one of thesereplacements can alter your finalanswer by a decimal.*The circumference of a circle (likethe perimeter) is found by theformulaC= 2  π  r
6. 6. Let’sPractice!What is the area of a circle with radius = 10 in ?A = 2 π r2A = 2 (3.14) (10)2A = 628 in2The Area is 628 in2 .
8. 8. CUBE*Remember with a square, allthe sides are equal. The sameapplies to a cube, which ismade up of squares on allfaces.*Where two squares meet iscalled an edge. The cornersare called vertices.The formula for Volume of aCube is V= s3 ( Volume = side3)s
9. 9. CUBETo find the Surface Area of a Cube, you need to find the sumof all the faces. To do this you can use a net, or layout of thefaces. For a cube, you are adding the areas of 6 squares, ormultiplying the area of one square by 6.Here is a formula for the Surface Area of a Cube, SA = 6 s2Practice!For a cube with edge = 7 in, what is the surface area?SA = 6  (7 in)2 The surface area is 294 in2 .
10. 10. RECTANGULAR PRISM*A rectangular prism is made up withrectangles for each face.The formula for Volume of aRectangular Prism is V= l  w  h (Volume = length  width  height )l (length)w(width)h(height)
11. 11. RECTANGULAR PRISMTo find the Surface Area of aRectangular Prism, you can usethe net, and add together all thefaces.You can also use theformula:SA= 2  ( w  h + l  w + l h)
12. 12. Let’sPractice!For a rectangular prism with length=5 in, width= 7 in and height = 3 in,what is the surface area?SA = 2 ( 7 in  3 in + 5 in  7 in + 5 in  3 in )SA = 2 ( 21 in2 + 35 in2 + 15 in2 )SA = 2 ( 71 in2 )SA = 142 in2 The Surface Area is 142 in2 .5 in7 in3 in
13. 13. PYRAMIDS*A pyramid is classified by the sides beingtriangles. The type of pyramid is determined by thebase. A triangular pyramid has a base that is atriangle. A square pyramid has a base that is asquare.
14. 14. PYRAMID*The height of the pyramid is theperpendicular line from the apex (thevertex where the sides of the trianglesmeet at the top of the pyramid) to thebase.*The slant height is the height of oneof the triangles on the side as if it werea 2D triangle.The formula for Volume of apyramid is V = 1/3  A  h(Volume = 1/3  Area of the base height of the pyramid )apexbaseheightslantheight
15. 15. TRIANGULAR PYRAMIDThe Surface Area of a triangularpyramid can be found by using thenet, and adding the areas of all thetriangular faces.It can also be found using theformula SA = B + ½  P  l( Surface Area = Base Area + ½ Perimeter of the base  slantheight )
16. 16. Given a triangular pyramid with base sides = 10 cm and slant height =5 cm, what is the surface area?B = ½ bh P = 30 cm SA = 25√3 + ½(30)(5)B = ½ (10)(5√3) SA = 25√3 + 75 cm2B = 25√3 cm2The Surface Area is 25√3 + 75 cm2 .10cm5 cmLet’sPractice!
17. 17. SQUARE PYRAMIDThe formula for Volume of a pyramid isstill V = 1/3  A  h(Volume = 1/3  Area of the base  heightof the pyramid )The formula for theSurface Area of a Square Pyramid isSA = 2  b  s + b2( Surface Area = 2  side of the base slant height + side of the base2 )
18. 18. TRIANGULAR PRISMA triangular prism has twotriangles and three rectangles. It isimportant to know if the trianglesare equilateral, which affects if therectangles are equal.The formula forVolume of a Triangular PrismisV = ½ (b  h)  l
19. 19. TRIANGULAR PRISMThe formula forSurface Area of a TriangularPrism is SA = b  h + 2  l  s +l  bHowever for a triangular prism itis easiest to find the surfacearea using a net. Find the areaof each side and add themtogether.
20. 20. There are so many moreshapes to explore! Stay tunedfor more…And Keep Practicing!