A plane figure with ten straight sides and angles i.e.,


There are some coins in the shape of decagon, which are the real life examples of Decagon.



The mediator who helps buying and selling of houses, sites, vehicles etc., is called commission agent or broker.

The money that the broker or agent receives in the deal is called brokerage or commission.

Commission is calculated on the transaction amount in percentage.

Commission per hundred rupees is called commission rate.

Commission = Commission rate ×S.P

Selling price = 100/commission rate   ×𝑐𝑜𝑚𝑚𝑖𝑠𝑠𝑖𝑜𝑛.

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A congruence relation (or simply congruence) is an equivalence relation.

Let a, b, m € Z and m ≥ 2. Then ‘a’ is said to be congruent to ‘b’ modulo m if m|(a – b) i.e., a ≡ b (mod m) ⇔ m|(a – b) 

For a given positive integer n, two integers a and b are called congruent modulo.  



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Central Angle

A central angle is an angle whose apex (vertex) is the center O of a circle and whose legs (sides) are radii intersecting the circle in two distinct points A and B.

The central angle is subtended by an arc between those two points, and the arc length is the central angle (measured in radians) times the radius.

Central Angle
∠AOB is the central angle of the circle with the centre O.


The circumference of a circle is the distance around it or it is the distance around the edge of a circle


To find the circumference of the circle:

Circumference, C = 2Πr, where r is the radius of the circle.



A circle is the locus of all points equidistant from a central point.

A circle is named by its centre, therefore, we call a circle O if its centre is named as O.

For example,

A circle with centre O is called circle O.

To find the area of the circle:

Area of the circle, A = Πr² , where r is the radius of the circle.

Cartesian coordinate system

A Cartesian coordinate system, also known as collier coordinate system, is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length.


Cartesian Coordinate System