1. Mensuration Formulae

2. Perimeter Formulae for Polygons

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

4. 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

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

6. 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)

7. 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

8. 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

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

10. 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

11. How can we find the relationship between the circumference of a circle and its diameter?

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. Archimedes, said C ≈3.1419 x d Early Attempts
Egyptian Scribe Ahmes. in 1650 B.C. said C≈ x d
Archimedes, said C ≈ 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≈ forever….

16. Videos on Circles http://www.youtube.com/watch?v=eiHWHT_8WrE
A Rap about circles
Circle Song2

17. 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

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. 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 = 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

23. 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 = 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