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Ch 4

Ch 4 . Measuring Prisms and Cylinders . Area of a Rectangle . To find the area of a rectangle, multiply its length by its width. A = l x w. How do you find the area. So, the area is 8.36 cm 2 . Area of a Triangle .

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Ch 4

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  1. Ch 4 Measuring Prisms and Cylinders

  2. Area of a Rectangle • To find the area of a rectangle, multiply its length by its width. • A = l x w

  3. How do you find the area • So, the area is 8.36 cm2.

  4. Area of a Triangle • To find the area of a triangle, multiply its base by its height, then divide by 2. • Remember the height of a triangle is perpendicular to its base. • The formula for the area of a triangle can be written:

  5. . How do you find the area Substitute b = 12 and h = 3. So, the area is 18 m2.

  6. Watch Brainpop: Area of Polygons • http://www.brainpop.com/math/geometryandmeasurement/areaofpolygons/preview.weml

  7. Area of a Circle • To find the area of a circle, use the formula: • A = r 2 • where r represents the radius of the circle • Recall that  is a non-terminating and a non-repeating decimal number. So, any calculations involving  are approximate. • You need to use the  function on your calculator to be more accurate – 3.14 is not accurate enough.

  8. How do you find the Area Use A = r 2. Substitute r = 6 ÷ 2 = 3. So, the area is about 28 mm2.

  9. Circumference of a Circle • The perimeter of a circle is named the circumference.The circumference is given by: C = d or C = 2r (Recall: d = 2r)

  10. Find the circumference of the circle. The circumference of the circle is about 22 cm.

  11. Find the radius of the circle. • The circumference of a circle is 12.57 cm • To find the radius of the circle, divide the circumference by 2. The radius of the circle is about 2 cm.

  12. Watch Brainpop: Circles • http://www.brainpop.com/math/geometryandmeasurement/circles/preview.weml • http://www.youtube.com/watch?v=lWDha0wqbcI

  13. Try It • Workbook pg 74 – 75 • Puzzle Package

  14. Activating Prior Knowledge: Words to Know

  15. Watch Brainpop: Review • http://www.brainpop.com/math/numbersandoperations/pi/preview.weml • http://www.brainpop.com/math/geometryandmeasurement/polygons/preview.weml • http://www.brainpop.com/math/geometryandmeasurement/polyhedrons/preview.weml • http://www.brainpop.com/math/geometryandmeasurement/typesoftriangles/preview.weml

  16. 4.1 Exploring Nets http://www.youtube.com/watch?v=y0IDttNW1Wo&feature=related

  17. A Prism • A prism has 2 congruent bases and is named for its bases. • When all its faces, other than the bases, are rectangles and they are perpendicular to the bases, the prism is a right prism. • A regular prism has regular polygons as bases.

  18. Which one is a Right Prism? YES No

  19. Pyramid • A regular pyramid has a regular polygon as its base. Its other faces are triangles. They are named after its base. Regular OctagonalPyramid Regular Pentagonal Pyramid Regular Square Pyramid

  20. Describe the faces of: • ACube • 6 congruent squares • A Right Square Pyramid • 1 square, 4 congruent isosceles triangles • A Right Pentagonal Prism • 2 regular pentagons, 5 congruent rectangles

  21. Nets • A net is a diagram that can be folded to make an object. A net shows all the faces of an object • http://www.senteacher.org/wk/3dshape.php

  22. Nets • A net is a two-dimensional shape that, when folded, encloses a three-dimensional object. http://www.youtube.com/watch?v=9KXuaT18Jyw&feature=related (quick) • The same 3-D object can be created by folding different nets. • You can draw a net for an object by visualizing what it would look like if you cut along the edges and flattened it out. • http://www.youtube.com/watch?v=rMNa9wICWbo&feature=related

  23. 4.2 Creating Objects From Nets

  24. Turn to p. 178 of Textbook This diagram is not a rectangular prism! Here is the net being put together

  25. p. 178 of TextbookExample #1a 2 congruent regular pentagons 5 congruent rectangles

  26. p. 178 of TextbookExample #1b 1 square 4 congruent isosceles triangles

  27. p. 178 of TextbookExample #1c This net has 2 congruent equilateral triangles and 3 congruent rectangles. The diagram is a net of a right triangular prism. It has equilateral triangular bases.

  28. p. 178 of TextbookExample #1d This is not a net. The two triangular faces will overlap when folded, and the opposite face is missing. Move one triangular face from the top right to the top left. It will now make a net of an octagonal pyramid.

  29. p. 179 of TextbookExample #2

  30. 4.3 Surface Area of a Right Rectangular Prism

  31. What is Surface Area? • Surface area is the number of square units needed to cover a 3D object • It is the sum of the areas of allthe faces of an object

  32. Finding SA of a Rectangular Prism • The SA of a rectangular prism is the sum of the areas of its rectangular faces. To determine the surface area of a rectangular prism, identify each side with a letter. • Rectangle A has an area of • A = l x w • A = 4 x 5 • A = 20 • Rectangle B has an area of • A = l x w • A = 7 x 5 • A = 35 • Rectangle C has an area of • A = l x w • A = 7 x 4 • A = 28 C B A

  33. Finding SA of a Rectangular Prism • To calculate surface area we will need 2 of each side and add them together • SA = 2(A) + 2(B) + 2(C) • SA = 2(l x w) + 2(l x w) + 2(l x w) • SA= 2(4 x 5) + 2(7 x 5) + 2(4 x 7) • SA = 2(20) + 2(35) + 2(28) • SA = 40 + 70 + 56 • SA = 166 in2 C B A

  34. Finding SA of a Rectangular Prism • Another Example • SA = 2(A) + 2(B) + 2(C) • SA = 2(l x w) + 2(l x w) + 2(l x w) • SA= 2(8 x 10) + 2(7 x 8) + 2(10 x 7) • SA = 2(80) + 2(56) + 2(70) • SA = 160 + 112 + 140 • SA = 412 units2 C B A

  35. Finding SA of a Rectangular Prism • You Try • SA = 2(A) + 2(B) + 2(C) • SA = 2 (l x w) + 2(l x w) + 2 (l x w) • SA= 2(15 x 6) + 2(10 x 6) + 2(10 x 15) • SA = 2(90) + 2(60) + 2(150) • SA = 180 + 120 + 300 • SA = 600 cm2 C B A

  36. Some Video Reminders • http://www.youtube.com/watch?v=oR1ukNC1pvA • http://www.youtube.com/watch?v=agIV623B3nc&feature=related

  37. Practice • Pg p.186 • #4, 6,7,10,12,13,15

  38. 4.4 Surface Area of a Right Triangular Prism

  39. Surface area of a Right Triangular Prism • To calculate the surface area of right triangular prism, draw out the net and calculate the surface area of each face and add them together.

  40. Surface area of a Right Triangular Prism • Draw and label the net 20cm 16cm D 16cm 20cm 12cm 10cm B 10cm C 10cm A D 16cm 20cm

  41. Surface area of a Right Triangular Prism • SA = A area + B area + C area + 2 D area • SA = A(l x w) +B(l x w) + C(l x w) + 2 * D[(b x h) ∕ 2)] • SA = A(16 x 10) + B(10 x 12) + C(20 x 10) + 2 * D[(16 x 12) ∕ 2] • SA = 160 + 120 + 200 + (2 * 96) • SA = 160 + 120 + 200 + 192 • SA = 672 cm2 20cm 16cm D 16cm 20cm 12cm 10cm B 10cm C 10cm A D 16cm 20cm

  42. Surface area of a Right Triangular Prism • Draw and label the net 10cm 6cm D 6cm 10cm 8cm 15cm B 15cm C 15cm A D 6cm 10cm

  43. Surface area of a Right Triangular Prism • SA = A area + B area + C area + 2 D area • SA = A(l x w) + B(l x w) + C(l x w) + 2 * D[(b x h) ∕ 2)] • SA = A(15 x 6) + B(15 x 8) + C(15 x 10) + 2 * D[(6 x 8) ∕ 2] • SA = 90 + 120 + 150 + (2 * 18) • SA = 90 + 120 + 150 + 36 • SA = 396 cm2 10cm 6cm D 6cm 10cm 8cm 15cm B 15cm C 15cm A D 6cm 10cm

  44. Surface area of a Right Triangular Prism • Draw and label the net 2.7m 1.4m D 1.4m 2.7m 2.3m 0.7m B 0.7m C 0.7m A D 1.4m 2.7m

  45. Surface area of a Right Triangular Prism • SA = A area + B area + C area + 2 D area • SA = (la x wa) + (lb x wb) + (lc x wc) + 2[(ld x wd) ∕ 2)] • SA = (1.4 x 0.7) + (0.7 x 2.3) + (2.7 x 0.7) + 2 [(1.4 x 2.7) ∕ 2] • SA = 0.98 + 1.61 + 1.89 + 2(1.89) • SA = 8.26m2 2.7m 1.4m D 1.4m 2.7m 2.3m 0.7m B 0.7m C 0.7m A D 1.4m 2.7m

  46. Surface area of a Right Triangular Prism • Draw and label the net ? m 3m D 3m ?m 8cm 7 m B 7 m 7 m C 7 m A D 3cm ?m

  47. Surface area of a Right Triangular Prism • Before you can solve, you need to find the missing side using Pythagorean Theorem! ? m 3m D 3m ?m 8cm 7 m B 7 m C 7 m A D 3cm ?m

  48. Surface area of a Right Triangular Prism • Pythagorean Theorem • a2 + b2 = h2 • 32 + 82 = h2 • 9 + 64 = h2 • 73 = h2 • √73 = √ h2 • 8.54 = h 8.54m 3m 8.54m 3m 8m 7 m 7 m 7 m 3m ?m

  49. Surface area of a Right Triangular Prism • SA = A area + B area + C area + 2 D area • SA = A(l x w) + B(l x w) + C(l x w) + 2 * D[(l x w) ∕ 2)] • SA = A(3 x 7) + B(7 x 8) + C(8.54 x 7) + 2 * D[(3x 8) ∕ 2] • SA = 21 + 56 + 59.78 + (2 * 12) • SA = 21 + 56 + 59.78 + 24 • SA = 160.78 m2 8.54m 3m D 8.54m 3m 8m 7 m B C 7 m 7 m A D 3m ?m

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