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

Perimeter Formulae for Polygons

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

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

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

Formulas for Quadrilaterals Name Shape Perimeter Area Square P=4b A=b2 Rectangle P=2b+2h =2(b+h) A=bh Parallelogram Rhombus Trapezium A=1/2(b1+b2)

Area of a triangle Area = ½ base x height or in algebraic form A= ½ bh 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

Examples 7cm 8cm 6cm 10cm Area =½ base X height 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

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

This means APPROXIMATELY EQUAL TO 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

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

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

Archimedes, said C ≈3.1419 x d 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????

The exact value is…………… UNKNOWN!!

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

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

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

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

Finding a formulae for the area of a circle

C= πd or C=2πr Semi-circle=πr πr r

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

The Area and Perimeter of a Circle A circle is defined by its diameter or radius radius The perimeter or circumference of a circle is the distance around the outside The area of a circle is the space inside it Diameter The ratio of π (pi) π is an irrational number whose value to 15 decimal places is π = 3.14159265358979.... We usually say π≈3.14 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

The Area and Perimeter of a Circle A circle is defined by its diameter or radius radius The perimeter or circumference of a circle is the distance around the outside The area of a circle is the space inside it Diameter The ratio of π (pi) π is an irrational number whose value to 15 decimal places is π = 3.14159265358979.... We usually say π≈3.14 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