Formulae . Perimeter Formulae for Polygons.
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Transcript of Formulae . Perimeter Formulae for Polygons.
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 circumference
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?
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….
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
