Regular Polygons & GeoGebra
Kids, No More Shame! GeoGebra Comes To School! GeoGSeries# Episode #01
Hi, last day, my son comes to me with these 10 math exercises to solve:/
I use this:
https://www.geogebra.org/classic/k5zb3twm.
Are you curious about what is GeoGebra? Welcome!
There you have it all math questions:
EX_01: A square inscribed on a circumference has an area worth 12 square meters; How big is the side of this square? What is its radius?
EX_02: a square inscribed on a circumference with the radius equal to r = 3+(ROOT(36)/2); tell us, under these conditions, what is the measure of the apothem and length of the side of this polygon?
EX_03: Given a regular hexagon inscribed on a circumference and knowing that this hexagon has a side equal to 4.5cm and apothem equal to 39/10; tell us, what is the area of that hexagon?
EX_04: Determine the measure of the central angle, the interior angle, and the number of diagonals of the following regular polygons: a) triangle; b) Heptagon, and c) Decagon?
EX_05: It is known that:
a) The circumference has a radius of 6cm;
b) the triangle (SOR) has an area of 17.12cm^2.
The question is: what is the measure of the shaded area of the figure?
EX_06: Check V for true and F for false to the alternatives below:
a)( ) Is the diagonal of a polygon a line segment that joins opposite vertices of a polygon?
b)( ) If the side of a square is 15cm, then its area is equal to 60cm^2?
c)( ) If the apothem of a regular pentagon is equal to 8.3cm and the side of the pentagon is equal to 12cm, then the perimeter of that pentagon is 60cm.
d)( ) the formula to find the area of a circle is equal to A = pi times diagonal?
e)( ) Is the central angle of a polygon equal to the measure of the interior angle?That one is just made of questions. Just playing around with GeoGebra to get it easily!
EX_07: a pendulum of 15cm in length oscillates between points A to B describing an angle of 15°. What is the length of the path described by its end between A and B?
EX_08: determine the size of an arc with a central angle measuring 22° contained in a circumference of radius equal to 10cm.
EX_09: Determine, in centimeters, the area of the figure below:
EX_10: Having a 10cm radius pizza, Maria ate a 35° circumference ring; in relation to that, say, what area of the pizza did Maria eat?
Oops! You know what? How far back can your memory go?
I find out that I am not able to complete this assignment within a tight timeframe…
It took me all day long to solve it by hand :/
Here’s How To Fix That: GeoGebra!
That’s it!
And this post is all about GeoGebra!
GeoGebra has become the leading provider of dynamic mathematics software, supporting science, technology, engineering, arts, and mathematics (STEAM*) education and innovations in teaching and learning worldwide (see its Awards and Abouts).
*STEAM (Science, Tech, Engineer, Art, and Math)Call GeoGebra anytime!
Never again will we forget anything or even that blessed apothem’s formula…
Just like a math pro, with these quick and easy steps, that I present now, we’ll solve these math problems in a way that you can never imagine it is possible to (and will give you the power to make infinite others questions, to leverage your child’s study!):
In 5 minutes!
Ooh, yeah! say what? say what? say what?
Five minutes! That’s it! Yeah, it is really amazing!
This is a real challenge that I impose on myself! Be my guest!
Trigger Chrono now!
A cool welcome!
00 #Step — See the solution for all problems here:
There is something excellent in GeoGebra, impressive really!
Let me show you how to get started quickly in a step-by-step fashion!
01 #Step — Ex_01 Solved!
EX_01: A square inscribed on a circumference has an area worth 12 square meters; How big is the side of this square? What is its radius?
(1) Set n to 4;
(2) Looking for the Area(egon*), then (3) reset the r until you get 12 as the value of the area of the polygon (or approximation; use the arrow in the keyboards to get as close as possible!) ;
*egon = Abstract Regular Polytopes (a geometric object with flat sides) - Egon Schulte(4)The result of the Length of a side of the egon is 3.46 and (3) the radius is 2.45.
Let’s confirm it by the formulas provided:
For calculation of the Area of the comics:
02 #Step — EX_02 Solved!
EX_02: a square inscribed on a circumference with the radius equal to r = 3+(ROOT(36)/2); tell us, under these conditions, what is the measure of the apothem and length of the side of this polygon?
(1) Set r to 6;
(2) There you have it: The Apothem is 4.24!
(3) The length of the side of the square is 8.49!
Let’s confirm it by the formulas provided:
For calculation of the Apothem & and length of this polygon:
03#Step — EX_03 Solved!
EX_03: Given a regular hexagon inscribed on a circumference and knowing that this hexagon has a side equal to 4.5cm and apothem equal to 39/10; tell us, what is the area of that hexagon?
(1) Set n to 6;
(2) Now reset the r until you get the Apothem to 3.9 and the Radius will be 4.5;
(3) There you have it: The Area of the hexagon is 52.61!
Let’s confirm it by the formulas provided:
For calculation of the Apothem & Perimeter:
04 #Step — EX_04 Solved!
EX_04: Determine the measure of the central angle, the interior angle, and the number of diagonals of the following regular polygons: a) triangle; b) Heptagon, and c) Decagon?First for the Triangle:
(1) Set n to 3 and (2) r to 10 for better visualization :);
(3) There you have it: The Triangle Central Angle is 120°!
(4) There you have it: The Triangle Interior Angle is 60°!
(5) There you have it: The Triangle N° of Diagonals is Zero!
Now for the Heptagon:
(1) Set n to 7;
(2) There you have it: The Heptagon Central Angle is 51.43°!
(3) There you have it: The Heptagon Interior Angle is 128.57°!
(4) There you have it: The Heptagon N° of Diagonals is 14!
Now for the Decagon:
(1) Set n to 10;
(2) There you have it: The Decagon Central Angle is 36°!
(3) There you have it: The Decagon Interior Angle is 144°!
(4) There you have it: The Decagon N° of Diagonals is 35!
Let’s confirm it by the formulas provided:
05 #Step — EX_05 Solved!
EX_05: It is known that:
a) The circumference has a radius of 6cm;
b) the triangle (SOR) has an area of 17.12cm^2.
The question is: what is the measure of the shaded area of the figure?The Pentagon:
(1) Set n to 5 and r to 6;
(2) There you have it: The Conic Area 113.1!
(3) There you have it: The Polygon Area 85.6!
(4) There you have it: The Remaining areas 27.5!
Let’s confirm it by the formulas provided:
6 #Step — EX_06 Solved!
Just playing with GeoGebra and you can answer those questions in a few seconds …Try it yourself!
EX_06: Check V for true and F for false to the alternatives below:
a)( V ) Is the diagonal of a polygon a line segment that joins opposite vertices of a polygon?
b)( F ) If the side of a square is 15cm, then its area is equal to 60cm^2?
c)( F ) If the apothem of a regular pentagon is equal to 8.3cm and the side of the pentagon is equal to 12cm, then the perimeter of that pentagon is 60cm.
d)( F ) the formula to find the area of a circle is equal to A = pi times diagonal?
e)( F ) Is the central angle of a polygon equal to the measure of the interior angle?07#Step — EX_07 Solved!
EX_07: a pendulum of 15cm in length oscillates between points A to B describing an angle of 15°. What is the length of the path described by its end between A and B?
08#Step — EX_08 Solved!
EX_08: determine the size of an arc with a central angle measuring 22° contained in a circumference of radius equal to 10cm.
09#Step — EX_09 Solved!
EX_09: Determine, in centimeters, the area of the figure below:Here is the answer to the Area_1 is 9.24!
And here is the answer to Area_2 is 2.96!
This question at first seemed easy, but maybe I was wrong…
It turned out to be a bit complicated … but Geogebra solved it! Check it out!
10#Step —EX_10 Solved!
EX_10: Having a 10cm radius pizza, Maria ate a 35° circumference ring; in relation to that, say, what area of the pizza did Maria eat?
This is kidStronics!
I am J3, The Arduino Hobbyist! Your host!
I hope that you as a teacher or parent, like me, have realized the potential of using this incredible tool in class or at home: GeoGebra!
Now please consider opening an account there!
It’s fast and I bet you’ll become an instant fan!
Enjoy it!
Thank You For Reading This Post!
Comments? Welcome any of them: positive or negative! interact more, please!
See you in the next #GeoGSeries Episode!
By for now o/
Download All Files for This Project
References & Credits
Regular Polygons by wikipedia.org
Egon Schulte by https://en.wikipedia.org/wiki/Egon_Schulte
Online Calculator by https://www.calculatorsoup.com/calculators/geometry-plane/polygon.php
Related Posts:
01# Episode — GeoGSeriesRegular Polygons & GeoGebra — Kids, No More Shame! GeoGebra Comes To School! (this one, for while:)
