Friday, October 19, 2012

Number of Quadrilaterals

Introduction to number of quadrilaterals:

A quadrilateral is a polygon with four sides or edges and four vertices or corners
Quadrilaterals are either simple (not self interesting).simple quadrilaterals are either convex or concave.
Plane is a shape which consist of four sides, and consequently four angles.

Description about Number of Quadrilaterals :
Quadrilaterals are classified into the following types

They are:

Trapezium

Parallelogram

Rhombus

Rectangle

Square

Kite

Number of Quadrilaterals with Example:
Square :

The square is one of the best example for quadrilaterals. It is defined by sides are equal, and its sum of  interior angles of all right angles should be (90°). and its opposite sides will be parallel.
we can say square is a specific case of regular polygin, in this case there are  4 number of sides. All the facts and properties described for regular polygons apply to a square.
Rectangle:

The rectangle is somwhat similar to the square, and this is one of the most generally known quadrilaterals. It is defined by having all four interior angles 90° (right angles).
Parallelogram

A quadrilateral has both pairs of opposite sides parallel and equal in length.
Parallelogram is defined by opposite sides are parallel and it should be congruent. It is the the root way  of some other quadrilaterals, which are consisting by adding some restrictions of various techniques:
A rectangle is a parallelogram but all the angles fixed at 90°
A rhombus is a parallelogram but with all sides equal in length
A square is a parallelogram but with all sides equal in length and all angles fixed at 90°.
Trapezoid

A quadrilateral should have  at least one pair of parallel sides
Rhombus:

In rhombus, the number of sides are four and its all equal.
Rhombus is looking like a special type of parallelogram. Iin a parallelogram, each sets of opposite sides are equal in length. but in rhombus, all four sides are the same length.so the properties are also same.
Rhombus is somewhat light similar ro square but the angles will not be 90o
Kite

A quadrilateral which contains  two distinct pairs of equal adjacent sides.
kite is a part of the quadrilateral relations, and while easy to understand visually, is a little tricky to define in precise mathematical terms. It has two pairs of equal sides. Each pair must be adjacent sides (sharing a common vertex) and each pair must be distinct. That is, the pairs cannot have a side in common.

Tuesday, October 16, 2012

Base of a Polygon

Introduction to base of polygon:

Let us discuss the base of polygon. The base of the polygon is declaring the lowest part. The base is commonly known as bottom line of the shape. Solid objects are placed on a plane by the bottom line of the surface. The straight side shape is called  the base of a polygon. Next we see the polygon base. For example in triangle we take one of the sides as base (from three sides). Similarly in square we take one of the sides of a base (from four sides).

Base of the Polygon

The two dimensional polygons are any side can be declare a base. There is the polygon “sits” bottom side is normally known as the base. The triangle is also known as the polygon. The three side polygon called as the triangles. We can say any side of triangle is base of the triangle. The all type of triangle contains three bases. The following diagram is representing the base of the polygons.

`Base = (2A)/(h)`           

The formula for the base of the triangle polygon is b = 2A / h. The b is representing the base of   the triangle. A is represent the area of the triangle. The h is representing the height of the triangle. Next we see the base of rectangle.

The rectangle is another part of the polygons. The rectangle polygons is represented the four sides. The base of the rectangle is declaring the bottom side of the diagram. The general formula for base of rectangle is b = A / h. the b is represents the base of the rectangle polygon. The A is represents the area of the rectangle polygon. The h is represents the height of the polygons.

`Base = (A)/(h)`

I am planning to write more post on How to Construct a Triangle, Properties of Quadrilaterals. Keep checking my blog.

Other Polygon Base

The next polygon declares the parallelogram. The side of the parallelogram is four. The base of the parallelogram is specifying the bottom side of the diagram. The general formula for base of parallelogram is b = A / h. the b is represents the base of the parallelogram polygon. The A is represents the area of the parallelogram polygon. The h is represents the height of the parallelogram polygons.

`Base = (A)/(h)`

Monday, October 15, 2012

These Form the Bases of a Prism

Introduction :

The prisms are the shapes that exist in the three dimensions. All the prisms are formed by the two bases and the bases of the prism formed by the faces of the prism. Regular polygons form the bases of a prism. In the following article we will discuss more about the online Volume of Right Prism help in detail.


More about the Topic these Form the Bases of a Prism

As we described before the prisms are the shapes formed by the two bases the upper base and the lower bases. All bases of the prism are the regular polygons and these form the bases of the prism. In the right regular prisms the bases of the prism are equal. The area of the bases is calculated as the product of the perimeter fo the base and the height of the prism. And the Formula for the area of the bases of the prism and the area of the total prism including the faces of the prism with the base made of n sides and side length S are,

Area of a base of the prism = `[n*S^2*cot (pi/n)]/4`

Total surface area = `[n*S^2*cot (pi/n)]/2 + S*H*n`



Example Problems on these Form the Bases of a Prism:

1. Calculate area of the base and the total area of the hexagonal prism with the height 10cm and side length of the base 5cm.

Solution:

Area of a base of the prism `= [n*S^2*cot (pi/n)]/4`

`= [6*5^2*cot (pi/5)]/4`

`= 43 cm^2`

Total surface area `= [n*S^2 cot (pi/n)]/2 + S*H*n `

`= [6*5^2*cot (pi /6)]/2 + 6*5*10`

`= (48*1.732) + 300`

`= 129.93 + 300`

`= 429.93 cm^2`

Practice problems on these form the bases of a prism:

1. Calculate area of the base and the total area of the pentagonal prism with the height 10 cm and side length of the base 6cm.

Answer: Total surface area = 423.9 cm2 and Area of a base= 61.94 cm2.

2. Calculate area of the base and the total area of the octagonal prism with the height 9cm and side length of the base 3cm.

Answer: Total surface area = 302.9 cm2 and Area of a base = 43.46 cm2.