Geogebra/C3/Mensuration/English
Title of script: Mensuration in Geogebra
Author: Madhuri Ganapathi
Keywords: Segment between two points, Circle with center and radius, Ellipse, Polygon, New point and Center, Insert text Area, Perimeter, Surface area, Volume, concatenation, Text box, input bar, video tutorial.
| Visual Cue | Narration |
|---|---|
| Slide Number 1 | Hello everybody
Welcome to this tutorial on Mensuration in Geogebra. |
| Slide number 2
Learning Objectives |
In this tutorial, we will learn to find
|
| Slide number 3
Pre-requisites |
We assume that you have the basic working knowledge of Geogebra.
For Revelant tutorials on Geogebra, Please visit our website |
| Slide Number 4
System Requirement |
To record this tutorial I am using Ubuntu Linux OS Version 11.10 Geogebra Version 3.2.47.0 |
| Slide Number 5
Tools used in the tutorial |
We will use the following Geogebra tools
|
| Switch to Geogebra window
Dash home>> Media Apps>>Eduaction>>Geogebra |
Let's open a new Geogebra window.
Click on Dash home and Media Apps. Under Type, choose Education and Geogebra |
| Let's find the area of a rhombus.
Let's use the file quadrilateral.ggb of the previous tutorial | |
| “File”>>Open”>>rhombus.ggb | Click on File, Open click on quadrilateral.ggb
click on 'Open' |
| Area of the Rhombus =1/2 * product of diagonals | Area of the Rhombus =1/2 * product of diagonals |
| To demonstrate it | |
| Click “Insert text” tool | Click on the “Insert text” tool |
| Click on the drawing pad | |
| “Area of rhombus=" + (1 / 2 g f) | A text box opens
“Area of the rhombus =”+(1/2 g f) |
| In the text box type | Open the double quotes(“) type
Area of the rhombus = close the double quotes '+' for concatenation open the brackets type '1/2' space 'f' space 'g' close the bracket 'f' and 'g' are diagonals of the rhombus |
| Click Ok.
Point to the Area of rhombus |
Click Ok.
Area of rhombus is displayed here on the drawing pad. |
|
Click “Insert text” tool |
Next, let's find Perimeter
Click on the “Insert text” tool |
| Click on the drawing pad. | Click on the drawing pad. |
| “Perimeter of the rhombus =”+(4a) | A text box opens.
“Perimeter of the rhombus =”+(4 a) |
| In the text box type | Open the double quotes(“) type
Perimeter of the rhombus = close double quotes '+' open the brackets '4' space 'a' close the brackets 'a' is side of the rhombus |
| Click Ok.
Point to perimeter of rhombus |
Click Ok.
Perimeter of rhombus is displayed here on the drawing pad. |
| Click on "Save As" >> type "rhombus-area-perimeter" in filename >> click on Save | Lets save this file now.
Click on “File” and "Save As". I will type the filename as "rhombus-area-perimeter" Click on “Save”. |
| Slide Number 6
Assignment 1 |
To find area and perimeter of trapezium, use output of file “cons-trapezium.ggb” Rename object 'g' as 'b' Formula for area = (half sum of parallel sides) * (vertical height) = (a+b)/2* h Formula for perimeter =(sum of the sides) =(a+b+c+d) |
| Show the output of the Assignment | The output of the assignment should look like this. |
| Click on “File” >> “New” | Let's open a new Geogebra window to draw a sphere
Click on “File” , “New” |
| Click “Circle with center and radius” tool | Click on “Circle with center and radius” tool from the toolbar |
| Click on the drawing pad point 'A' | |
| Dialog box opens >>type value '2' for the radius | A text box opens.
enter value '2' for radius. |
| Click OK | Click OK
A circle with center 'A' and radius '2cm' is drawn. |
| Click New point tool >>mark point 'B' | Select “New point” tool from tool bar mark a point 'B' on the circumference of the circle |
|
Click “Segment between two points” tool>> join 'A' and 'B' |
Select “Segment between two points” tool
Join points 'A' and 'B' as radius of the circle |
| Let's draw an ellipse “CDE” in the horizontal direction,
to touch the circumference of the circle. | |
| Click “Ellipse” tool>>touch the circumference | Click on “Ellipse” tool from tool bar |
| Mark points 'C' , 'D' 'E' | Mark points 'C' and 'D' diagonally opposite to each other on the circumference
and a third point 'E' inside the circle Here a sphere is drawn |
|
Click on “Insert text” tool |
Let's now find the Surface area of the sphere
Click on “Insert text” tool |
| Click on the drawing pad. | Click on the drawing pad. |
|
Scroll down the list to find π (pi) |
A text box opens
Please use drop down list in the text box for special characters Scroll down the list to find π (pi) |
| Type in the text box >>
“ Surface area of the sphere =” +( 4 π a^2) |
“ Surface area of a sphere =” +( 4 π a2) |
| Type in the text box | open double quote type
Surface area of the sphere = close double quote 'plus' open the bracket '4' space select 'π' from the list space 'a' select 'square' from the list close the bracket |
| Click OK | Click OK
surface area of the sphere is displayed here let me click on it and drag it place it below |
| Next let's find Volume | |
|
Insert another text box |
Click on the 'Insert Text' tool |
| click on the drawing pad
Text box opens | |
| Type in text box >>“Volume of the sphere =” +(4/3 π a^3) | “ Volume of the sphere =” +(4/3 π a^3) |
| Type in the text box | open double quote type
Volume of the sphere = close double quote 'plus' open the bracket '4/3' space select 'π' from the list space 'a' select 'cube' from the list close the bracket |
| click OK | click OK
Volume of the sphere is displayed here let me click on it and drag it to place it below |
| Next let's draw a cone now | |
|
Click Polygon tool>>Click on 'C' , 'D', 'F' and 'C' |
Click on “Polygon” tool
Click on points 'C' , 'D' and an external point 'F' and 'C'once again |
| Click Segments between two points >> join points A and F | Select “Segments between two points” tool
to join points 'A' and 'F' We get height of the cone. |
|
Right click on the object>>select “Rename” Replace 'b with 'h' |
Let me rename object 'b' as 'h' which denotes height of the cone
Right click on object 'b' Click on “Rename” Replace 'b' with 'h' click OK |
| Right click on the object>>select “Rename”>>replace c_1 with 's' | Let me also
Rename the object 'c_1' as 's' which denotes slant height of cone. Right click on 'c_1' click on “Rename” Replace 'c_1' with 's' Click OK |
| Let's find now surface area and volume of the cone,
We can use either the Insert text tool from the tool bar or we can the input bar. I will use the “Input bar” | |
|
Scroll down the list. Click on “π” |
Please find the special characters in the drop down list of “Input bar” Scroll down to find “π” |
| Type in the input bar >> Area = (π a s + π a²) | Area = (π a s + π a²)
Type in the input bar |
| Type in the 'Input bar' | Surfacearea = open the bracket
Select 'π' from the list space 'a' space 's' plus select 'π' from the list space 'a'
press enter
|
| Point to the Algebra View | Area of the cone is displayed in the Algebra view
Please note when we use the Input bar answer appears in the Algebra view |
| Let's find Volume | |
| Type in the input bar>>
Volume =(1/3 π a² b) |
Volume =(1/3 π a² h) |
| Type in the 'Input bar' | Volume =open bracket
'1/3' space select 'π' from the list space 'a' Select 'square' from list space 'h' close the bracket Press enter |
| Point to the Algebra view | Volume of the cone will be displayed here in the Algebra view |
| Click on "Save As" >> type "Sphere-cone" in filename >> click on “Save” | Lets save this file now. Click on "Save As".
I will type the filename as "Sphere-cone" Click on “Save”. with this we come to the end of this tutorial |
| Slide Number 7
Summary
|
Let us summarize
In this tutorial we have learnt to find
We have also learnt to draw sphere and cone |
| Slide Number 8
Assignment |
Assignment
As an assignment I would like you to find Surface area and volume of cylinder Draw 2 same sized ellipses one below the other Connect edges of ellipses Use “center” tool, find center of one ellipse Join center and edge. Rename object 'b' as 'h' and 'e' as 'r' Surface area = 2 π r(r + h) Volume = π r^2h |
| Show the output of the Assignment | The output of the assignment should look like this. |
| Slide number 7
Acknowledgement |
Watch the video available at
http://spoken-tutorial.org/What is a Spoken Tutorial It summarises the Spoken Tutorial project If you do not have good bandwidth, you can download and watch it |
| The Spoken Tutorial Project Team :
Conducts workshops using spoken tutorials Gives certificates to those who pass an online test For more details, please write to contact@spoken-tutorial.org | |
| Spoken Tutorial Project is a part of the Talk to a Teacher project
It is supported by the National Mission on Education through ICT, MHRD, Government of India More information on this Mission is available at http://spoken-tutorial.org/NMEICT-Intro ] This is Madhuri Ganapathi from IIT Bombay signing off. Thanks for joining |
