Online Geometry Book

Introduction:

Geometry is a construction of object according to our given measurement. Geometry books contains the collection of object  which could be square, rectangle, triangle, circle, parallelogram, cone, cylinder, cube, prism, quadrilateral. Basic geometry concepts are plane, points, rays, lines, line segment, type of lines and  angles. Main purpose of using geometry is finding area,  volume and surface of given object it may be two dimensional or three dimensional object.


Standard formulas for geometric figures:

Two dimensional objects:

Square:

Perimeter of square = 4 * side
Area of square = side * side
Rectangle:

Area of rectangle = Length x width
Perimeter of rectangle = 2(Length + Width)
Triangle

Area of triangle = `1/2` (Base* height)
Perimeter of triangle = (sum of three sides)
Parallelogram

Area of parallelogram = length × breadth
Circle problems:

Area of circle = ? r2 , where r is the radius.
Circumference of triangle = 2 * ? * r
Diameter = 2 * Radius
Three dimensional objects:

Three dimensional objects are: Cone, sphere, cylinder, hemisphere, prism

Volume of cylinder = ? * R2 * h
Volume of a right circular cone = `1/3`   * ?  * R3
Volume of a sphere  = `4/3` * ? * R3
Volume of a hemisphere = `2/3` * ? * R3

Example problems:


Example 1: Find the area and perimeter of square when the side length is 5cm?

Solution:

Area of square    = (side * side)

= 5 * 5

= 25cm^2

Perimeter of square = 4 * side

= 4 * 5 = 20 cm

Example 2: Find the area and perimeter of rectangle with length 4cm, width 3 cm?

Solution:

Area of rectangle = Length x width

= 4 * 3

= 12cm^2

Perimeter of rectangle = 2(Length + width)

= 2(4 + 3)

= 14cm

Example 3: Find the area of triangle base is 4cm,height is 2cm

Solution:

Area = `1/2` (4 * 2)

= `8/2`

= 4cm^2

Example 4: Find perimeter of triangle whose side lengths are 5cm, 5cm, and 8cm?

Solution:

Perimeter = (A + B + C) (Sum of three side lengths)

A = 5, B = 5, C = 8

= (A + B + C) (Sum of three sides)

= 5 + 5 + 8 = 18cm

Example 5: Find the area and circumference of the circle when the radius is 4cm?

Solution:

Area = `pi`

= 3.14 * 4 * 4

= 50.24cm^2

Circumference = 2 * ? * r

= 2 * 3.14 * 4

= 25.12cm

Example 6: Find the area of rhombus whose diagonals are 6cm and 9cm

Solution:

Area of rhombus =`1/2` (diagonal1 * diagonal2)

= `1/2`  ( 6 * 9)

= 27cm^2

Example 7: Find the volume of cylinder whose diameter of the base is 10 cm, height is 10 cm?

Solution:

Diameter of the base is 10 cm,

Radius = `10/2`

Radius(R) = 5cm

V = Area of the base × Height = `pi` * R * R * H

= 3.14 * 5 * 5 * 40

= 3140cm^2