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## Ch 4

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**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 cm2.**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:**.**How do you find the area Substitute b = 12 and h = 3. So, the area is 18 m2.**Watch Brainpop: Area of Polygons**• http://www.brainpop.com/math/geometryandmeasurement/areaofpolygons/preview.weml**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.**How do you find the Area**Use A = r 2. Substitute r = 6 ÷ 2 = 3. So, the area is about 28 mm2.**Circumference of a Circle**• The perimeter of a circle is named the circumference.The circumference is given by: C = d or C = 2r (Recall: d = 2r)**Find the circumference of the circle.**The circumference of the circle is about 22 cm.**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.**Watch Brainpop: Circles**• http://www.brainpop.com/math/geometryandmeasurement/circles/preview.weml • http://www.youtube.com/watch?v=lWDha0wqbcI**Try It**• Workbook pg 74 – 75 • Puzzle Package**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**4.1 Exploring Nets**http://www.youtube.com/watch?v=y0IDttNW1Wo&feature=related**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.**Which one is a Right Prism?**YES No**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**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**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**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**Turn to p. 178 of Textbook**This diagram is not a rectangular prism! Here is the net being put together**p. 178 of TextbookExample #1a**2 congruent regular pentagons 5 congruent rectangles**p. 178 of TextbookExample #1b**1 square 4 congruent isosceles triangles**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.**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.**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**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**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**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**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**Some Video Reminders**• http://www.youtube.com/watch?v=oR1ukNC1pvA • http://www.youtube.com/watch?v=agIV623B3nc&feature=related**Practice**• Pg p.186 • #4, 6,7,10,12,13,15**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.**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**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**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**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**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**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**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**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**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**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