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Mensuration Formulae

Mensuration Formulae. http://hench-maths.wikispaces.com. Perimeter Formulae for Polygons. Area of rectangle. Area= bh. h=height. b=base. Base is at RIGHT ANGLE to Height. Area of Square. A square is a rectangle with all equal sides Base=Height. Area= b 2. Height=Base=b. b=base.

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Mensuration Formulae

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  1. Mensuration Formulae http://hench-maths.wikispaces.com

  2. Perimeter Formulae for Polygons

  3. Area of rectangle Area= bh h=height b=base Base is at RIGHT ANGLE to Height

  4. Area of Square A square is a rectangle with all equal sides Base=Height Area= b2 Height=Base=b b=base

  5. Area of a Parralelogram Area= bh Base is at RIGHT ANGLE to Height

  6. Formulas for Quadrilaterals

  7. Area of a triangle height height base base The area of a triangle is equal to half the area of the rectangle that can be drawn with the same base and height. The Area of the triangle can thus be calculated using the formula Area = ½ base x height or in algebraic form A= ½ bh

  8. Examples 7cm 8cm 6cm 10cm Area =½ base X height = ½ x 10 x 8 = ½x80 =40 sq cm Area =½ base X height = ½ x 6 x 7 = ½x42 =21 sq cm

  9. What is the formula relating the circumference to the diameter? circumference centre Diameter Radius

  10. C = ? x d People knew that the circumference is about 3 times the diameter but they wanted to find out exactly. C ≈ 3 x d This means APPROXIMATELY EQUAL TO

  11. How can we find the relationship between the circumference of a circle and its diameter?http://arcytech.org/java/pi/measuring.html

  12. Complete these questions in your workbook Now that you have calculated all the ratios here are a few more questions: • Are the ratios close to your prediction? • How similar are the different ratios that you got? • Does the value of the ratio depend on the size of the circle? • What does all of this data analysis tells you? • What is the value of ? In C = ?xd

  13. Early Attempts Egyptian Scribe Ahmes. in 1650 B.C. said C≈3.16049 x d Archimedes, said C ≈3.1419 x d Fibonacci. In 1220 A.D. said C≈3.1418xd What is the value of the number that multiplies the diameter to give the circumference????

  14. The exact value is…………… UNKNOWN!!

  15. An approximation to π π≈3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609................forever….

  16. Videos on Circles • http://www.youtube.com/watch?v=eiHWHT_8WrE • A Rap about circles http://www.youtube.com/watch?v=fogehnFNDw0&feature=related • Circle Song2 http://www.youtube.com/watch?v=lWDha0wqbcI&feature=related

  17. What about the AREA of a circle? 2r First consider a square The area of this square in terms of r is A= 2r x2r = 4r2 r 2r

  18. What about the AREA of a circle? Now consider a circle inside the square The area of the circle must be less than the are of the square A < 4r2 2r r 2r Area = ? xr2

  19. Finding a formulae for the area of a circle

  20. C= πd or C=2πr Semi-circle=πr πr r

  21. Area of Rectangle= Base x Height Area = πr x r Area =πr2

  22. A circle is defined by its diameter or radius The Area and Perimeter of a Circle The perimeter or circumference of a circle is the distance around the outside radius The area of a circle is the space inside it Diameter The ratio of π (pi) The circumference is found using the formula C=π d or C= 2πr (since d=2r) The area is found using the formula A=πr2

  23. A circle is defined by its diameter or radius The Area and Perimeter of a Circle The perimeter or circumference of a circle is the distance around the outside radius The area of a circle is the space inside it Diameter The ratio of π (pi) The circumference is found using the formula C=π d or C= 2πr (since d=2r) The area is found using the formula C=πr2

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