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# Polygons, Circles, Triangles

Polygons, circles and triangles these are the very important topics in geometry. These are also used in coordinate geometry, trigonometry etc like topics. They are geometrically represented as below:

## How to find Triangle type

There are three types of triangles they are,

Acute triangles (all sides are acute i.e. less than 90$^o$),

Obtuse triangles (one angle is obtuse i.e. more than 90$^o$),

Equilateral triangles (all sides are equal),

Right triangles (one of the angle is 90$^o$),

Isosceles triangles (two sides are equal), and

Scalene triangles (no sides are equal).

A quadrilateral is a polygon with four sides and with four vertices or corners. We generally have two types of quadrilaterals they are regular and irregular, the area of a general quadrilateral can be calculated using a simple formula.

Where AC and BD are diagonals and they are calculated using cross product and they are also calculated using the formulas,

$\frac{1}{2}$[AC X BD]

Where AC = (x1,y1) and BD = (x2,y2)

$\frac{1}{2}$[x1y2 - x2y1]

where the lengths of the diagonals are p and q and the angle between them is $\theta$

$\frac{1}{2}$[pqsin$\theta$]

where the lengths of the diagonals are p and q and the angle between them is $\theta$

[x1y2 - x2y1]

where the lengths of the diagonals are p and q and the angle between them is $\theta$

$\frac{1}{2}$[pqsin$\theta$]

where the lengths of the diagonals are p and q and the angle between them is $\theta$

There are 6 types of quadrilaterals they are square, rectangle, parallelogram, trapezoid, rhombus and kite. They are represented as shown below:

## Circle Facts

A circle is a set of points in a plane that are all the same distance from a fixed point. This fixed point is called the center and the set of points form the circumference.

A radius is a line segment joining the center of the circle to a point on the circumference.

A chord is a line segment joining two points on the circumference. A chord divides a circle into two segments, the larger being the major segment and the smaller the minor segment.

A diameter is a chord that passes through the center of a circle; a diameter is 2 times of radius i.e. d = 2r.

An arc of a circle is a portion of its circumference. A sector is the region enclosed by two radii and an arc. Two radii divide a circle into two sectors: a major sector and a minor sector.

A tangent line to a circle is a line that touches the circumference but does not cross it. The angle between a tangent line and the radius at the point of contact is 90°.

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## Polygon Shapes

There are n number of polygon shapes here are some polygon shapes from: Triangle – 3 sides

Square – 4 sides, Pentagon – 5 sides, Hexagon – 6 sides, Heptagon – 7 sides, Octagon – 8 sides, Nonagon – 9 sides, Decagon – 10 sides, Hendecagon – 11 sides, Dodecagon – 12 sides.