Formulae

http://hench-maths.wikispaces.com

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????

The exact value is……………

UNKNOWN!!

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