PERIMETER,AREA AND VOLUME

1. The perimeter of a polygon (or any other closed curve, such as a circle) is the distance around the outside.

2. The area of a simple, closed, planar curve is the amount of space inside.

3. The volume of a solid$3\text{D}$ shape is the amount of space displaced by it.

Perimeter formula
Square	4 × side
Rectangle	2 × (length + width)
Parallelogram	2 × (side1 + side2)
Triangle	side1 + side2 + side3
Regular n-polygon	n × side
Trapezoid	height × (base1 + base2) / 2
Trapezoid	base1 + base2 + height × [csc(theta1) + csc(theta2)]
Circle	2 × pi × radius
Ellipse	4 × radius1 × E(k,pi/2) E(k,pi/2) is the Complete Elliptic Integral of the Second Kind k = (1/radius1) × sqrt(radius12 - radius22)
Area formula
Square	side2
Rectangle	length × width
Parallelogram	base × height
Triangle	base × height / 2
Regular n-polygon	(1/4) × n × side2 × cot(pi/n)
Trapezoid	height × (base1 + base2) / 2
Circle	pi × radius2
Ellipse	pi × radius1 × radius2
Cube (surface)	6 × side2
Sphere (surface)	4 × pi × radius2
Cylinder (surface of side)	perimeter of circle × height
	2 × pi × radius × height
Cylinder (whole surface)	Areas of top and bottom circles + Area of the side
	2(pi × radius2) + 2 × pi × radius × height
Cone (surface)	pi × radius × side
Torus (surface)	pi2 × (radius22 - radius12)
Volume formula
Cube	side3
Rectangular Prism	side1 × side2 × side3
Sphere	(4/3) × pi × radius3
Ellipsoid	(4/3) × pi × radius1 × radius2 × radius3
Cylinder	pi × radius2 × height
Cone	(1/3) × pi × radius2 × height
Pyramid	(1/3) × (base area) × height
Torus	(1/4) × pi2 × (r1 + r2) × (r1 - r2)2

MATHS-THE WORLD OF WONDER

MIRACLES OF GEOMETRIC SHAPES

MATHS IN DAILY LIFE - EXAMPLES OF FIBONACCI SEQUENCES

PUZZLES

Maths  puzzles

 

1.       What 5-digit number has the following features: 
 If we put the numeral 1 at the beginning, we get a number three times smaller than if we put the numeral 1 at the end of the number

Solution;

We can make an equation:
3(100000 + x) = 10x+1
Solving this gives:
10x+1 = 3(100000 + x)
10x+1 = 300000 + 3x
10x = 299999 + 3x
7x = 299999
x = 299999/7 = 42857
The answer is 42857 (142857 is three times smaller than 428571)

2.      How can I get the answer 24 by only using the numbers 8, 8, 3 and 3?

You can use add, subtract, multiply, and divide.

Solution;

 8/ (3-(8/3))
= 8/(1/3)
= 24

3.      When asked about his birthday, a man said:

"The day before yesterday I was only 25 and next year I will turn 28."

This is true only one day in a year - when was he born?

Solution:

He was born on December 31st and spoke about it on January 1st.
The day before yesterday I was only 25...'
Dec 30: 25
Dec 31: 26
Jan 1 (this year): 26

'...next year I will turn 28'
Dec 31 (this year): 27
Dec 31 (next year): 28

4.      Use exactly four 4's to form every integer from 0 to 10, using only the operators +, -, x, /, () (brackets),  (decimal point), x² (square), square root and ! (factorial).
Example: 0 = 44-44

 Solution:

0 = 44-44
1 = 44/44 or (4+4)/(4+4) or (4/4) / (4/4) or [(4! - 4)/ 4] - 4
2 = 4/4+4/4
3 = (4+4+4)/4
4 = 4*(4-4)+4
5 = (4*4+4)/4
6 = 4*.4+4.4
7 = 44/4-4
8 = 4+4.4-.4
9 = 4/4+4+4   

10= 44/4.4
 

STUDY TOUR