mensuration formulae
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Perimeter Formulae for Polygons
Area of rectangle
b=base
h=heightArea= bh
Base is at RIGHT ANGLE to Height
Area of Square
b=base
Height=Base=bArea= b2
A square is a rectangle with all equal sides Base=Height
Area of a Parralelogram
Area= bh
Base is at RIGHT ANGLE to Height
Name Shape Perimeter Area
Square P=4b A=b2
Rectangle P=2b+2h
=2(b+h)
A=bh
Parallelogram A=bh
Rhombus P=4b A=bh
Trapezium A=1/2(b1+b2)
Formulas for Quadrilaterals
Area of a triangle
The area of a triangle is equal to half the area of the rectangle that can be drawn with the same base and height.
base base
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
height
Examples
10cm
8cm
6cm
7cm
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
Diameter
Radius
centre
What is the formula
relating the circumferenc
e to the diameter?
People knew that the circumference is about 3 times the diameter but they wanted to find out exactly.
C = ? x d
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:
1. Are the ratios close to your prediction?
2. How similar are the different ratios that you got?
3. Does the value of the ratio depend on the size of the circle?
4. What does all of this data analysis tells you?
5. What is the value of ? In C = ?xd
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????
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?2r
2rr
First consider a square
The area of this square
in terms of r is
A= 2r x2r = 4r2
What about the AREA of a circle?2r
2r
Now consider a circle inside the square
The area of the circle must be less than the are of the square
A < 4r2
r
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 CircleA circle is defined by its diameter or radius
Diameter
radi
usThe perimeter or circumference of a circle is the distance around the outside
The area of a circle is the space inside it
The ratio of π (pi)diameter
ncecircumfere
π is an irrational number whose value to 15 decimal places is π = 3.14159265358979.... We usually say π≈3.14The 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 CircleA circle is defined by its diameter or radius
Diameter
radi
usThe perimeter or circumference of a circle is the distance around the outside
The area of a circle is the space inside it
The ratio of π (pi)diameter
ncecircumfere
π is an irrational number whose value to 15 decimal places is π = 3.14159265358979.... We usually say π≈3.14The 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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