Polygon

Let Us Learn About Polygons

Few names of polygons are as follows:

• Triangle or Trigon

This is a three-sided shape that having whole interior angle measurement as 180º.

• Quadrilateral or Tetragon

This is a four-sided shape that having whole inside angle measurement as 360º.

• Pentagon

This is a five-sided shape which contains the whole inside angle measurement as 540º.

The polygon is a closed path. The polygon has the different shapes. The shapes are depends on the number of sides. The Straight lines are form the polygon shapes. The polygons are having more number of straight lines to form the different polygons. Angles of the polygons are varied based on shape of the polygon.

The area of the regular polygon can be written as,

Area = S² N / 4 tan (pi / N).

Here, S = Length of any side, N = Number of side, Pi = 3.14.

Area of the Polygons

1) The given length of side:

Area Shape of polygon = S² N / 4 tan (Pi/N)

Here, S = Side length, N = Number of side, Pi = 3.14.

2) Given the radius(circum radius):

Area shape of polygon = (R² N sin (2Pi/N))/2.

Here, R = Radius of the polygon, N = Num

ber of side, Pi = 3.14.

3) Given the apothem (In radius):

Area Shape of polygon = A² N tan (Pi/N).

Here, A = Apothem length, N = Number of sides.

4) Given the apothem and Length of a side:

Area shape of polygon = A* P / 2.

Here, A = Apothem length, P = Perimeter.

More about Polygon:

Basic diagrammatic representation for polygon is as follows:

Polygon- A polygon is a closed figure made by joining line segments, where each line segment intersects exactly two others.

Regular Polygon- A regular polygon is a polygon whose sides are all the same length, and whose angles are all the same.

Quadrilateral- A four-sided polygon. The sum of the angles of a quadrilateral is 360^o.

Rectangle- A four-sided polygon having all right angles. The sum of the angles of a rectangle is 360^o.

Square- A four-sided polygon having equal-length sides meeting at right angles. The sum of the angles of a square is 360^o.

Parallelogram- A four-sided polygon with two pairs of parallel sides. The sum of the angles of a parallelogram is 360^o.

Rhombus- A four-sided polygon having all four sides of equal length. The sum of the angles of a rhombus is 360^o.

Trapezoid- A four-sided polygon having exactly one pair of parallel sides. The two sides that are parallel are called the bases of the trapezoid. The sum of the angles of a trapezoid is 360^o.

.Pentagon- A five-sided polygon. The sum of the angles of a pentagon is 540^o.

Hexagon- A six-sided polygon. The sum of the angles of a hexagon is 720^o.

Octagon- An eight-sided polygon. The sum of the angles of an octagon is 1080^o.

Nonagon- A nine-sided polygon. The sum of the angles of a nonagon is 1260^o.

Decagon- A ten-sided polygon. The sum of the angles of a decagon is 1440^o.

Convex- A figure is convex if every line segment drawn between any two points inside the figure lies entirely inside the figure. A figure that is not convex is called a concave figure.

Area of a square = side x side

= s x s

= s² sq units or units²

Area of a Rectangle = length x width

= l x w

= lw sq units or units²

Area of a Parallelogram= base x height

= b x h

= bh sq units or units²

Area of a Triangle = ½ x base x height

= ½ b h sq units or units²

Area of a Rhombus = base x height

= b x h

= bh sq units or unit²

Area of a Trapezoid = ½ (a+b)h sq units or units²

(Half of the sum of the lengths of the Parallel sides times height)

Polygon

Let Us Learn About Polygon

A polygon is a closed figure that is the union of line segments in a plane. A polygon has three or more sides. A polygon has the same number of angles as sides.

Polygons can be classified as either convex or concave.

A polygon is convex if no line that contains a side of the polygon contains a point in the interior of the polygon. In a convex polygon, each interior angle measures less than 180 degrees.

Concave polygons "cave-in" to their interiors, creating at least one interior angle greater than 180 degrees (a reflex angle).

Unless otherwise stated, we will be discussing convex polygons.

Listed below are some of the more commonly used polygons.

Types Of Polygon

A polygon is equilateral if all of its sides are of the same length.
A polygon is equiangular if all of its angles are of equal measure.

A regular polygon is a polygon that is both equilateral and equiangular.

Sum of Interior Angles of a Polygon = 180(n-2)

Each interior angle of a "regular" polygon = 180(n-2)/n

Sum exterior angles of any polygon = 360° (using one exterior angle at a vertex)

Each exterior angle (regular polygon) = 360/n

Standard Polygons:

The different standard polygons are:

1. Square

2. Rectangle

3. Parallelogram

4. Triangle

5. Rhombus

6. Trapezium / Trapezoid

Regular Polygon

Definition of Regular Polygon

• A polygon having all its sides equal and all the angles equal is called a Regular Polygon.

More about Regular Polygon

• The measure of each angle of a regular polygon with n sides is given as(n-2) x 180/n degrees.
• A circumscribed circle can be drawn through all the vertices of a regular polygon.

Square Root

Let Us Learn About Square Root

To find the square root of a given number is to think of what number when multiplied by itself is equal to the given number.

For example, to find the square root of 4, we have to think of a number that when multiplied by itself gives 4. The number is 2 since 2 × 2 = 4.

So the square root of a given number is the positive number whose square produces the given number.

Properties of Square Roots:

• The product of two values in the square roots with different numbers inside it can be written in a single root in a product of those two root values.
• The number outside the square root symbol, when it gets into square root, it turns into a square of number.
• The square root of fraction value can be written as individual roots, as root in numerator and root in denominator separately.
• When a perfect square comes out of the square root symbol, it becomes the number without square root.

Square root is an radical symbol which is used in the mathematics. It is shown as the symbol as √. The number inside the radical symbol is called as the rubicund, for example if the given value is √x. The x is called as the rubicund which is the number inside the radical symbol √. There are more number of roots available depending upon the value we have. The roots are square root √x, cube root 3√x, Fourth root 4√x this up to nth root n√x. Here we are going to see about the square root of 16 and 17 in different methods of solving.

Let’s make it clear with some examples:

• √x * √y = √xy [By the first property]
• = x√y = √x2y [By the second property]
• √x/ y = √x/√y [By the third property]

Explain Ray in Geometry

Let us study about Ray,

A ray is also a piece of a line, except that it has only one endpoint and continues forever in one direction. It could be thought of as a half-line with an endpoint. It is named by the letter of its endpoint and any other point on the ray. The symbol → written on top of the two letters is used to denote that ray. This is ray AB (Figure 1).

Figure1 Ray AB.

It is written as

This is ray CD (Figure 2 ).

Figure 2 Ray CD.

It is written as or

Note that the nonarrow part of the ray symbol is over the endpoint.

Hope the above explanation helped you.

square root of complex number

Let us learn about square root,

A divisor of a quantity that when squared gives the quantity. For example, the square roots of 25 are 5 and -5 because 5 × 5 = 25 and (-5) × (-5) = 25.

A number that, when squared, yields a given number. For example, since 5 × 5 = 25, the square root of 25 (written 25) is 5.

"Roots" (or "radicals") are the "opposite" operation of applying exponents; you can "undo" a power with a radical, and a radical can "undo" a power. For instance, if you square 2, you get 4, and if you "take the square root of 4", you get 2; if you square 3, you get 9, and if you "take the square root of 9", you get 3:

Hope the above explanation helped you.