Geogebra/C3/Mensuration/English

Title of script: Mensuration in Geogebra

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

• Area and perimeter of rhombus
• Surface area of sphere and cone
• Volume of sphere and cone
Slide number 3

Pre-requisites

We assume that you have the basic working knowledge of Geogebra.

For Revelant tutorials on Geogebra,

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
• Segment between two points
• Circle with center and radius
• Ellipse
• Polygon
• New point and
• Insert text
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'

Select 'square' from list close the bracket

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

• Find Area and perimeter of rhombus
• Surface Area of sphere and cone
• Volume of sphere and cone

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 :

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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