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6.10

6.10. The student will Define pi ( π ) as a ratio of the circumference of a circle to its diameter b) Solve practical problems involving circumference and area of a circle, given the diameter or radius c) Solve practical problems involving area and perimeter

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6.10

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  1. 6.10 The student will Define pi ( π) as a ratio of the circumference of a circle to its diameter b) Solve practical problems involving circumference and area of a circle, given the diameter or radius c) Solve practical problems involving area and perimeter d) Describe and determine the volume and surface area of a rectangular prism

  2. Brain PopArea of Polygons

  3. Objective 6.10 is really in three sections. Here is an overview.Sections A and B and pi (π) 3.14 (we do this after Winter Break)area of circles A =πr² circumference of circles C = πdSection C (Before Winter Break)Area of squares A= lw or A= s² because squares have congruent sidesPerimeter of squares P= 4s or P= S+S+S+SP= 4(3) or 3+3+3+3 P= 12 inArea of rectangles A= lwA= 7 • 2 A = 14 square inches Perimeter of rectangles p = 2l + 2w or P= S+S+S+S P= 2(7) + 2(2) P= 14+4= 18 in Area of triangles A=½ bhor A=b•h÷2 A= ½ • 4 •3 A= .5•4•3 A= 6 inches squaredbecause triangles are ½ a square or rectangle Perimeter of triangles P= s+s+s P= 2 + 3 + 4 P= 9 inchesSection D (after Winter Break)Volume of a rectangular prism V = lwh Surface Area of a rectangular prism S.A. = 2lw + 2lh + 2wh A= 3² or A= 3 x 3 = 9 square inches 3 in 7 in 2 in 7 in 2 in 3 in h=3 in b=4 in 4 in 3 in 2 in

  4. Pg _____ 6.10c • Directions- MA and PA….multiply area and perimeter add. • Draw a picture of the situation to determine if it is area or perimeter. Label the measurements. Write formulas and solve • Key words- • Area- cover, carpet, grass, mow, an area, paint, tile • Perimeter- fence, trim, border, enclose, hem, edge, around • Examples • SQUARE • A= S² or A= lwP= 4s or P= s+s+s+s • A= 8 ² A=8• 8 P= 4(8) P= 8+8+8+8 • A= 64 in² A= 64 in² P= 32 in P= 32 in • RECTANGLE • A=lw P= 2l + 2w • A= 10 •6 P = 2(10) + 2(6) Or for perimeter just add all the sides • A= 60 in² P= 20 + 12 • P= 32 inches • TRIANGLE (remember that ½ is .5) • A=½ bhP= s+s+s • A= .5•6•7 • A= 15 in² 6.10c Vocabulary pg____ Polygon –A polygon is a simple, closed, two-dimensional figure formed by three or more sides. Area – It is the product of the length and the width (A = lw). The area of a triangle is one half of the measure of the base times the height: Perimeter –The perimeter of a polygon is the measure of the distance around the polygon. Length(l) - The measurement of the extent of something along its greatest dimension. Width(w) - The measurement of the extent of something from side to side. Base(b) – Bases are the top and bottom faces of a three-dimensional object. Height(h) –The shortest distance from the base of a parallelogram to its opposite side. ------------------------FORMULAS------------------- 8 in • Draw & Key Word Formula and Work Answer Area of squares A= lw or A= s² because squares have congruent sidesPerimeter of squares P= 4s or P= S+S+S+S Area of rectangles A= lwPerimeter of rectangles p = 2l + 2w or P= Area of triangles A=½ bhor A=b•h÷2 because triangles are ½ a square or rectangle Perimeter of triangles P= s+s+s 10 in 6 in H=7 in b=6 in

  5. 6.10c Practice pg- • Table cloth covers 6ft x 4 ft table. • 2. Sew a trim on a table cloth that is 6 ft x 4 ft. • 3. Paint a wall that is 10 ft x 8 ft. •  4. How much frosting for a triangular shaped cake that’s base 5 inches and height is 2 inches • 5. Sewing a ribbon arounda triangle with a base of 8 inches and two sides each 7 inches. pg 6.10c Practice Find the area of a 13cm x 9cm rectangle. Find the perimeter of a 20m x 10m rectangle. Find the area of a square with a 5 inch side Find the perimeter of a square with a 6 ft side Find the area of a triangle with a 7 mm height and a 8 mm base Find the perimeter of a triangle with the sides 1in, 2in, and 3 inch. • Draw & Key Word Formula and Work Answer • Draw & Key Word Formula and Work Answer • Draw & Key Word Formula and Work Answer • Draw & Key Word Formula and Work Answer • Draw & Key Word Formula and Work Answer • Draw & Key Word Formula and Work Answer • Draw & Key Word Formula and Work Answer • Draw & Key Word Formula and Work Answer • Draw & Key Word Formula and Work Answer • Draw & Key Word Formula and Work Answer • Draw & Key Word Formula and Work Answer

  6. 6.10c pg You will be asked to determine area with partial information. Draw the figures as shown. Label each square, then figure out the total length and width for each side. You plan to push three tables together for a party. For one table, the length is 8 ft and its width is 4 ft. All three tables are the same size. What is the total area once you push all three tables together? You can solve by figuring one table’s area and then multiplying by three Or determine the new length and width and then solve area 18 cm 8 ft 4 ft 3 cm 3 cm A=lw A=8 x 4 A= 32 ft² 32 ft 32ft 32 x 3= 96 ft² 3 3 3 3 3 3 12 cm 3 3 21 ft A= lw A= 18 • 12 A= 216 cm² 8 ft 4 ft 4 ft 4 ft A= lw A= 12 x 8 A= 96 ft² 7 ft 4 ft 7 7 4 16 ft 4 A=lw A=21•16 A= 336 ft² 4

  7. 1) Rectangle 3ft x 7ft • Area ______________Perimeter______ • 2) Triangle 14 cm base and 20 cm height • Area _____________Perimeter_______ • 3) Rectangle- • Each little square is • 4 cm x 4cm • Area ____________Perimeter__________ • 4) Triangle 5 inch base and 13 inch height • Area ___________Perimeter_________ • 5) Square 4 cm side •  Area ____________Perimeter________ • 6) Rectangle 5 yards x 7 yards • Area ___________Perimeter___________ • 7) Triangle 14 foot base and 15 foot height • Area _____________ • 8) Triangle 4.2 inch base and 14 inch height • Area ____________Perimeter___________ 4 cm 4 cm

  8. 6.10c Math Word Problems Area and Perimeter of 3 and 4 sided Polygons

  9. 1. Samantha owns a ranch that covers 48 square miles. She will plant wheat on all the land except for 16 square miles. Samantha will plant wheat on __________ square miles of land. a. 64b. 32c. 4d. 768 • Draw & Key Word Formula and Work Answer

  10. 2. A rectangle is 5 inches wide. The area of the rectangle is 35 square inches. What is the perimeter of the rectangle? a. 24 inchesb. 40 inchesc. 30 inchesd. There is not enough information to know. • Draw & Key Word Formula and Work Answer

  11. 3. John’s bedroom is exactly 18 feet by 21 feet. He wants to get carpeting to cover the entire floor. How many square yards of carpeting does he need? a. 126b. 378c. 13d. 42 • Draw & Key Word Formula and Work Answer

  12. Key Word Formula and Work Answer

  13. Draw & Key Word Formula and Work Answer

  14. 7. What is the area of triangle RST? R 5 in 13 in S 12 in T • Draw & Key Word Formula and Work Answer

  15. 8. What is the area of the large rectangle shown if each small square is 2 inches wide and 2 inches long?

  16. 10. Sam and Abby are covering their table with newspaper before beginning an art project. Their table is 48 inches by 60 inches. How many square inches of newspaper will they need? • Draw & Key Word Formula and Work Answer

  17. 11. The brown tiles that the kids of KFMS walk on,border a hall that is 80 foot long on each side (there are two sides). How many feet of brown tile is that? • Draw & Key Word Formula and Work Answer

  18. 12. June is painting her front door red. Her door is 8 ft by 3 ft. How any feet of paint will she need to cover the door? • Draw & Key Word Formula and Work Answer

  19. 13. A picture measures 5 inches by 5 inches. How much wood is needed to frame the picture? • Draw & Key Word Formula and Work Answer

  20. What is the area of the triangle? H-6 inches B- 10 inches • Draw & Key Word Formula and Work Answer

  21. 15. I am covering a triangular shaped slice of pie with whipped cream. How much whipped will cover the pie? b= 4 inches • Draw & Key Word Formula and Work Answer H=6 inches

  22. Holiday HouseUse the figuring box to answer each questionWhen you are finished answering the questions, you may decorate your house for the holidays! • Draw & Key Word Formula and Work Answer

  23. Answer the questions, then glue your answers on the back of construction paper. Next decorate your house. Finally, the outside fits over the inside on the front of your construction paper.

  24. Name_________________ 6.10 c Date___________ • It is time to decorate and get the house ready for holiday company! • 1. The kitchen floor needs to be retiled before every one comes to visit for the holidays. How many square feet of tile will you need to buy? • 2. The living room needs new carpet before the company arrives. How much carpet will you need to buy? • 3. You are planning to cover the front door with festive red foil paper. The door is 7 feet tall and 3 feet wide. How many square feet of foil paper will you need to cover the door? • 4. You are going to make a holiday tablecloth for your 3’ X 4’ table. How many square feet of material will you need to buy? • 5. You decided to add a holly trim to the edge of the tablecloth mentioned in question 4. How much holly will you need to buy? • 6. You are going to enclose the front porch with holiday lights. The porch is a rectangle that is 30 feet long and 6 feet wide. How many feet of lights will you need? • 7. You need to cover the couch cushions with a blanket because your brother is coming to visit for the holidays and has three BIG dogs he is bringing with him. What a mess they make! Your couch is 6 feet long and two feet wide. How much area does the blanket need to cover? • 8. Your flower garden is 10 feet by 3 feet and you would like to put a really neat lighted snowman border around it. How many feet of lighted snowmen will you need to buy? • 9. Next, the lawn needs to be mowed before everyone gets to your house. Your yard is 50’ X 70’. How many square feet will you have to mow? • 10. Finally, the last yard project is putting a fence up around your 50’ X 70’ yard to keep your brother’s three big messy dogs out of the street and chasing cars. How many feet of fencing will you need to buy to fence in your yard to keep those dogs out of trouble?

  25. 6.10 a and bArea and Circumference of Circleshttp://www.brainpop.com/math/numbersandoperations/pi/http://www.brainpop.com/math/geometryandmeasurement/circles/

  26. Pg 6.10 a and b Directions DR your circle If Radius given, double for diameter If Diameter given, halve for radius Ex- Determine what is being asked for, AREA or CIRCUMFERENCE 3. Write the formula and take one step at a time Area Circumference A= πx r x r C= π x d A= πr² C= πd A= 3.14 x 5² C= 3.14 x 10 A= 3.14 x 25 C= 31.4 in A= 328.5 in ² 6.10 a and b vocabulary pg 62 approximation An inexact result adequate for a given purpose ratio A comparison of two numbers by division. Example: The ratio 2 to 3 can be expressed as 2 out of 3, 2:3, or 2/3. circumference The distance around the outside of a circle (like perimeter) distance is a little over 3 times the diameter pi The ratio of the circumference of a circle to the diameter of a circle; equal to the fraction 22/7; often written as the approximation 3.14 radius The distance from the center of the circle to any point on the circle (half diameter) diameter The distance across a circle through the center (double radius) D- 10 R-5 D- 10 R-5 10 in 5 in

  27. Pg Practice Circumference Practice Area 6.10 a and b pg

  28. 6.10 dVolume and Surface Area of a Rectangular Prismhttp://www.brainpop.com/math/geometryandmeasurement/volumeofprisms/

  29. Pg ____ 6.10 d Examples: Surface Area- (measured in square units) SA=2lw+2lh+2wh Write this first l = 8 in. w = 12 in. h = 2 in. 6.10 d pg. Rectangular Prism Volume and Surface area Net - An arrangement of two-dimensional figures that can be folded to form a polyhedron Rectangular prism - A solid figure that has two parallel and congruent bases that are rectangles (a box) Volume - (fill) The number of cubic units needed to fill the space occupied by a solid. Answer is cubed. V=lwh Surface area - (cover) The sum of the areas of all the surfaces (faces) of a three-dimensional figure . Answer is squared. SA=2lw+2lh+2wh w=12 in h= 2 in l=8 in height length width SA = 2lw + 2lh + 2wh SA = 2(8)(12) + 2(8)(2) + 2(12)(2) SA = 2(96) + 2(16) + 2(24) SA = 192 + 32 + 48 SA = 272 inches² Volume (measured in cubic units) V=lwh Write this first l = 8 in. w = 12 in. h = 2 in. V=lwh V=(8)(12)(2) V=192 in³

  30. Pg____ 6.10 d Practice Determine the Surface Area for each Rectangular Prism 6.10 d Practice pg______ Determine the Volume for each Rectangular Prism 12 in 5 in 4 in 12 in 5 in 4 in 3 in 5 in 7 in 3 in 5 in 7 in 3 in 4 in 10 in 3 in 4 in 10 in

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