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SURFACE AREA

GEOMETRY 3D solid. SURFACE AREA. SOLID SHAPES AND THEIR FACES. SOLID FIGURE Enclose a part of space. COMPOSITE SOLID It is made by combining two or more solids. SOLID FIGURES. RECTANGULAR PRISM Will slide and stack. Faces of a rectangular prism. SOLID FIGURES.

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SURFACE AREA

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  1. GEOMETRY 3D solid SURFACE AREA

  2. SOLID SHAPES AND THEIR FACES SOLID FIGURE Enclose a part of space COMPOSITE SOLID It is made by combining two or more solids

  3. SOLID FIGURES RECTANGULAR PRISMWill slide and stack • Faces of a rectangular prism

  4. SOLID FIGURES CylinderWill roll, stack, and slide • Faces of a cylinder

  5. SOLID FIGURES PyramidWill slide • Faces of a pyramid

  6. SOLID FIGURES Cone Will roll and slide • Face of a cone

  7. SOLID FIGURES CubeWill slide and stack • Face of a cube

  8. SOLID FIGURES SPHEREWill roll

  9. Welcometothethe real word

  10. Welcometothethe real word

  11. Surface Area What does it mean to you?, Does it have anything to do with what is in the inside of figure? Surface area is found by finding the area of all the sides and then adding those answers up. How will the answer be labeled? Units2 because it is area!

  12. Surface Area Steps for Finding Surface Area 1. Draw and label each face of the solid as if you had cut the solid apart along its edges and laid it flat. Label the dimensions. 2. Calculate the area of each face. If some faces are identical, you only need to find the area of one. 3. Find the total area of all the faces.

  13. PRISMS

  14. PRISM In a prism, the bases are two congruent polygons and the lateral faces are rectangles or other parallelograms.

  15. PRISM PYRAMID In a prism, the bases are two congruent polygons and the lateral faces are rectangles or other parallelograms. In a pyramid, the base can be any polygon. The lateral faces are triangles.

  16. Top Back Side 2 Side 1 Front Bottom Rectangular Prism Top Back Side 2 Side 1 Front Bottom

  17. Rectangular Prism Net H B H B H B B H H B H H B

  18. Surface Area of a Prism Calculate the area of each face. If some faces are identical, you only need to find the area of one. Then, find the total area of all the faces. Example: Find the surface area of this rectangular prism It is made by: 2 congruent bases, and 4 lateral faces Surfacearea 180 m2 Base area = 2(6 x 8) = 96 m2 Lateral surfacearea (front and back) = 2 (3x6) = 36 m2 Lateral surfacearea (sides) = 2 (3x8) = 48 m2 Surfacearea = 96 + 36 + 48 = 180 m2

  19. B C 5 in A 6 in 4 in Rectangular Prism How many faces are on here? 6 Find the area of each of the faces. Do any of the faces have the same area? If so, which ones? Opposite faces are the same. Find the SA A = 5 x 4 = 20 x 2 = 40 B = 4 x 6 = 24 x 2 = 48 C = 6 x 5 = 30 x 2 = 60 Surface Area = 40 + 48 + 60 = 148 in2 Surface Area of a Rectangular Prism 2A + 2B + 2C

  20. Triangular Prism

  21. Triangular Prism Net

  22. Triangular Prism How many faces are there? 5 5 4 10 m 3 How many of each shape does it take to make this prism? 2 triangles and 3 rectangles = SA of a triangular prism Find the area of the 3 rectangles. Find the area of the triangle. Front 5 x 10 = 50 Back 4 x 10 = 40 Botton 3 x 10 = 30 120 4 x 3/2 = 6 x 2 = 12 2 How many triangles were there? Area of bases + area of laterals = SA 12 + 120 = SA What is the final SA? SA = 132 m2

  23. Cube Are all the faces the same? YES How many faces are there? 6 Find the Surface area of one of the faces. 4m 4 x 4 = 16 Take that times the number of faces. x 6 96 m2 SA for a cube. Surface Area of a Cube = 6 a 2

  24. CYLINDERS

  25. Cylinder

  26. Cylinder Net

  27. Surface Area of a cylinder • The two bases are circular regions, so you need to find the areas of two circles • The lateral surface is a rectangular region • The height of the rectangle is the height of the cylinder • The base of the rectangle is the circumference of the circular base Example: Find the surface area of the cylinder It is made by: 2 congruent circles, and 1 rectangle Circlearea= 3.14 (5)2 78.5 x 2  157 in2 Lateral area= (2 x 3.14 x 5 )12 376.8 in2 b= c = 2 r h= 12 Cylindersurfacearea = 157 + 376.8 = 533.8 in2

  28. Cylinders 3 What does it take to make this? 2 circles and 1 rectangle = SA cylinder 10m 2B + LSA = SA Surface Area of a Cylinder 2 circles (bases) 1 rectangle (Lateral) SA = 56.52 + 188.4 SA = 244.52

  29. CLASS WORK Find the surface area of each solid. All given measurements are in centimeters

  30. PYRAMID

  31. PYRAMID

  32. PYRAMID In a pyramid, the base can be any polygon. The lateral faces are triangles.

  33. PYRAMID SQUARE PYRAMID REGULAR N-GON PYRAMID Slant Height Altitude Slant Height Base Altitude Base

  34. PYRAMID SQUARE PYRAMID

  35. PYRAMID REGULAR N-GON PYRAMID

  36. PYRAMID Slantheight : It ist he height of each triangular lateral face. Itislabeledl The pyramid height is labeled h. The surface area of a pyramid is the area of the base plus the areas of the triangular faces(lateral area). SA = L+B Surface Area Base Area Lateral Area

  37. PYRAMID The surface area of a pyramid is the area of the base plus the areas of the triangular faces. What is the area of each lateral face? _1_bl 2 What is the total lateral surface area for any pyramidwith a regular n-gon base n . _1_bl 2 What is the area of the base for any regular n-gonpyramid? 1 aPor1 abn 2 2 The formula for the surface area of a regular n-gonpyramidin terms of n, base length b, slant height l, and apothem a. SA = 1 nb(l+a) 2

  38. PYRAMID The expression for the surface area of a regular n-gon pyramid in terms of height l, apothema, and perimeter of the base, P. SA= 1 P(l+a) 2

  39. PYRAMID The formulas to find the surface area of a pyramid are: SA = L+B Basic formula SA = 1 P(l+a) 2 SA = 1 nb(l+a) 2 or in terms of : n = number of triangular faces b = base length , l= slant heightand a = apothem in terms of : l = height, a = apothem, and , P = perimeter of the base.

  40. SPHERES

  41. Spheres • Sphere – The set of all points in space equidistant from a given point. Center Radius – Is a segment that has one end point at the center & the other end point on the sphere. r Diameter – A segment passing through the center w/ both end points on the sphere.

  42. Spheres SA = 4r2 r Radius of a sphere

  43. Spheres SA = 4r2 = 4(4)2 = 4(16) = 64 = 201.1m2 4m

  44. CONES

  45. CONES

  46. CONES lateral surface l l r Base = πr2 lateral surface= πrl

  47. CONES The surface area is the sum of the area of its base and the lateral (side) surface. l πr2 Find the area of the circle, or base Find the area of the curved (lateral) surface cone r πrl The surface area of the cone equals the area of the circle plus the surface area of the cone given by Where,r is the radiusl is the slant height

  48. Find the total surface area of the cone.

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