In geometry, area and perimeter of different shapes are two very important concept or term. In simple words, area means amount of space occupied by a shape. On the other hand, perimeter means boundary or outline of a shape.
Various formulas are used while calculating area and perimeter of different shapes. Detailed formulas are given below:-
Area of different shapes:-
(1) Square:- a²
(a= side of the square)
(2) Rectangle:- l×b
(l= length , b= breadth)
(3) Triangle:- ½ × b × h
(b= base , h= height)
(4) Circle:- πr²
(r= radius)
(5) Parallelogram:- b×h
(b= base , h= height)
(6) Rhombus:- ½ × (d1 × d2)
(d1= diagonal 1 , d2= diagonal 2)
(7) Trapezium:- ½ × (a+b) × h
(a and b = two parallel side , h= height)
Perimeter of different shapes:-
(1) Square:- 4× a
(a= side of the square)
(2) Rectangle:- 2 × (l + b)
(l= length , b= breadth)
(3) Circle:- 2πr
(r= radius)
(4) Triangle:- a + b + c
(a , b , c are sides of the triangle)
(5) Rhombus:- 4× a
(a= side of the rhombus)
(6) Trapezium:- a + b + c + d
(a , b , c , d are sides of Trapezium)
(7) Parallelogram:- 2 × (a + b)
(a and b = adjacent sides)
Basic facts about different geometrical shapes:-
Square:-
(1) Square has four sides.
(2) Four sides of square are equal in length.
(3) Square has four angles.
(4) Four angles of square are equal and measure 90⁰ each.
(5) Opposite sides of square are parallel.
Rectangle:-
(1) Rectangle has four sides.
(2) Opposite sides of rectangle are equal in length.
(3) Rectangle has four angles.
(4) Four angles of the rectangle are equal and measure 90⁰ each.
(5) Opposite sides of rectangle are parallel.
Triangle:-
(1) Triangle has three sides.
(2) Triangle has three angles.
(3) Summation of all three interior angles of a triangle is 180⁰.
Rhombus:-
(1) Rhombus has four sides.
(2) Four sides of rhombus are equal in length.
(3) Rhombus has four angles.
(4) Opposite angles of rhombus are equal.
(5) Opposite sides of rhombus are parallel.
Parallelogram:-
(1) Parallelogram has four sides.
(2) Opposite sides of parallelogram are equal in length.
(3) Parallelogram has four angles.
(4) Four angles of parallelogram are equal and measure 90⁰.
(5) Opposite sides of parallelogram are parallel.
Trapezium:-
(1) Trapezium has four sides.
(2) One pair of opposite sides of trapezium is parallel.
Circle:-
(1) A circle is a round shaped figure.
(2) Distance of all points of a circle from centre is equal.
(3) A circle has infinite number of radius.
(4) Diameter of a circle is a straight line passing through centre and touch two distinct point of a circle.
Parts of a circle :-
There are different parts in a circle, each with its own name, significance and properties. Some of these are given below:-
Radius :-
The length from the center of the circle to any point on the circumference of a circle is termed as the radius of that circle. It is constant in nature for any circle.
Diameter :-
Diameter is the straight line passing through the center of the circle and it connects two points on the circumference. The diameter is twice the length of the radius or the radius is half of the length of diameter.
Circumference :-
Circumference is the boundary of the circle or the distance around the circle.
Chord :-
Chord is a straight line segment which connects two points on the circumference but it may or may not pass through the center of the circle.
Centre :-
Circle is the centre point inside the circle. It is in equal distance from every point on the circumference.
Parts of square :-
Square consists of different parts. These are:-
Sides :-
A square has four sides. All four sides have the same length.
Vertices or Corners :-
A square has four vertices or corners. Measure of each vertex is 90 degree angle.
Angles :-
A square has four angles and each angle measures 90 degrees.Diagonals :- A square has two diagonals which have equal length.
Meaning of area:-
Area is the amount of space occupied by a geometrical shape. Area is always measured in square units , such as:- centimetre² (cm²), kilometre² (km²), meter² etc.
Meaning of perimeter:-
Perimeter is the length of boundary or outline of a geometrical shape. Perimeter is always measured in units , such as:- centimetre (cm), kilometre (km), meter etc.
These are basic formulas, which are used while calculating area and perimeter of different shapes. Basic understanding is essential, so basic concepts are given above. I hope these will help students.
Now the basic explanation of Pythagorean theorum is given below:-
The Pythagorean theorem is one of the basic principles in the field of geometry, which elaborate that in a right angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Expression of formula is:- a² = b² + c²
Here, (i) “a” and “b” are the lengths of the two sides of the triangle.
(ii) “c” is the length of the hypotenuse.
This theorem is useful for determining the length of an unknown side in right angled triangles when length of the other two sides are given or known.
Example:-
Suppose you have a right angled triangle with lengths of two sides are 3 and 4 units respectively, and now find the length of the hypotenuse.
Solution:-
Using the Pythagorean Theorem formula:-
a² = b² + c²
a² = 3²+ 4²
a² = 9 + 16
a² = 25
a = √25
a = 5
So, the length of the hypotenuse is 5 units.
Another example is given below for better understanding.
Example:-
Suppose you have a right angled triangle with lengths of one side is 5 units and the other side is unknown, and the length of the hypotenuse is 13. Find the length of the other side.
Solution:-
Using the Pythagorean Theorem formula:
a² = b² + c²
13² = 5² + b²
169 = 25 + b²
169 – 25 = b²
b² = 144
b = √ 144
b = 12
So, the length of the other side is 12 units.
Pythagorean theorum is very important theory and it is widely used in various fields such as physics, geometry, architecture etc .
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