Area Of Two Dimensional Shapes

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Dimension is a physical or mathematical space or object informally defined as the ''minimum number of co- ordinates required to specify each point within it " .

The shapes such as triangles and polygons has the dimension of two because it requires two co-ordinates to specify each point in it .

Each and every two dimensional shape has particular areas with the particular area finding formulas for the respective shapes .

Area of certain two dimensional shapes are mentioned below

1 . Area of the Triangle :

Triangle is a two dimensional figure . So area of the two dimensional shape such as triangles is given by

Area = 1/2 * b * h

where , b = base , h = height

2 . Area of the Square :

Square is a kind of two dimensional shape . So the area of the two dimensional shape such as square is given as follows

Area = s2

where , s = side of the square

3 . Area of the Rectangle :

Rectangle is also a two dimensional shape . So the area of such a two dimensional shape is given as follows

Area = l * w

where , l = length , w = width

Area ...
... of Parallelogram , Trapezoid and Circle

4 . Area of the Parallelogram :

Parallelogram is a two dimensional shape . The area of the two dimensional shape such as the parallelogram is

Area = b * h

where , b = base . h = height

5 . Area of the Trapezoid :

Trapezoid is also a two dimensional figure . The area of the Trapezoid is given by

Area = 1/2(b1+b2) * h

where , b1 and b2 are the bases of the trapezoid and h = height

6 . Area of the Circle :

Circle is a two dimensional figure . The area of the two dimensional shape such as circles is

Area = Πr2

where , r = radius

Area of Ellipse , Hexagon and Octagon

7 . Area of the Hexagon :

Hexagon is also a two dimensional shape . The area of the two dimensional Hexagon is

Area = Πr1r2

where , r1 = distance between center and semi - minor axis

r2 = distance between center and semi-major axis

8 . Area of Hexagon :

Hexagon is a two dimensional figure . The area of the two dimensional shape such as hexagon is

Area = (3√3/2 )r2

where , r = radius

9 . Area of the Octagon :

Octagon is a two dimensional shape . Its area is

Area = ( 2 + 2√2 )a2

where , a = length of the sides .

Three-dimensional space is a geometric model of the physical universe in which we live. The three dimensions are commonly called length, width, and depth (or height) although any three mutually perpendicular directions can serve as the three dimensions. In this article we shall see about some 3D shapes and how to calculate their properties.

Source -Wikipedia

Three Dimensional Shapes: Rectangular prism

A rectangular prism is one type of three dimensional geometric shape. It has six sides, which are rectangle in shape. In a rectangular prism all angles are right angle and opposite faces of rectangular solid are equal.

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Formula:

The volume of rectangular solid can be calculated by multiplying the length, width and height of rectangular solid.

Volume of rectangular solid (V) = length x width x height Cubic unit

= l x w x h cubic unit.

Example problem:

1. find the volume rectangular prism whose length 5cm width 3cm and height 8cm

Solution:

Given:

Length =5cm

Width =3cm

Height =8cm

Formula:

Volume of rectangular solid (v) = l x w x h

= 5 x 3 x 8

= 120

Volume of rectangular prism (v) = 120 cm3.

Three Dimensional Shapes: Cylinder and Cone

Cylinder is a three dimensional geometric shape. It has two parallel bases, which are circle shapes. The space occupied by the cylinder is known as volume of cylinder.

Fig No 2:

Formula:

The volume of the cylinder = π x r2 x h cubic unit

Example Problem:

1. The cylinder has the radius r= 11 cm, h=18 cm. find the volume of cylinder.

Solution:

Given:

r=11 cm

h=18cm

Formula:

The volume of the cylinder = π x r2 x h cubic unit

=3.14 x (11)2 x 18

= 6838.92cm3.
Cone:

It is one type of three dimensional geometric shape. Their base is in the form of circle and its side taper up to a point.

Fig No 3:

The volume of the cone =1/3 x π x r2 x h

Example problem for learn:

The cone has the radius = 7 cm and height = 10 cm. find the volume of the cone.

Solution:

Given:

Radius (r) = 7cm

Height (h) =10 cm

Formula:

The volume of the cone =1/3 x π x r2 x h

= 1/3 x 3.14 x (7)2 x 10

= 512.866 cm3

The volume of cone = 512.86cm3

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