Deriving Area Of Equilateral Triangle Using Basic Triangle Formula
Take an equilateral triangle of the side a units. Then draw a perpendicular bisector to the base of height h.
Deriving Area Of Equilateral Triangle
Now,
Area of Triangle = ½ × base × height
Here, base = a, and height = h
Now, apply Pythagoras Theorem in the triangle.
a2 = h2 + 2
Now, put the value of h in the area of the triangle equation.
Area of Triangle = ½ × base × height
A = ½ × a × ½
Or, Area of Equilateral Triangle = ¼
How To Draw Triangles In Python Turtle
Drawing with Turtle in Python is really fun. In the past handful of tutorials, we learned how to import the Turtle module for use in our programs saw how to make the turtle move on the canvas, made the turtle change directions on the canvas, saw how to use loops in turtle, and made drawings of shapes using variables. Now we will take a look at drawing another type of Polygon, the triangle using the Turtle library in Python.
Construct An Equilateral Triangle Inscribed In A Circle Proof
Think of that equilateral triangle as itself made up of three smaller isosceles triangles, sharing P , established by dividing the circle’s full 360 ° by 3 .
Each of these smaller isosceles triangles has two vertices on the circle and each shares congruent sides with the other triangles. That makes two of the three sides of the triangles congruent.
If two sides of an isosceles triangle are congruent, then the third side is, too, by the Side-Angle-Side theorem.
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Define A Triangle Function
To draw a triangle, we want to use a function, and it should make use of variables. We do this so that we can call the function many times if we like to draw many triangles of different sizes.
from turtle import *drawing_area = Screendrawing_area.setupshapedef draw_triangle: for i in range: forward leftdraw_triangledone
Nice! The triangle function works. Notice that the loop uses 3 iterations shown by range whereas when we drew a square it used 4 iterations in the loop. Another thing we notice is that we are passing in 120 as the degrees to turn for the left function. Why is that? This is because when drawing a triangle, you need to use the outside angle rather than the inside angle. What we are drawing here is an equilateral triangle since all three angles of an equilateral triangle add up to 180 degrees.
Drawing An Equilateral Triangle
Side AB is given. With A and B as centers and AB as radius, lightly construct arcs to intersect at C ” rel=”nofollow”>Figure 4.32a). Draw lines AC and BC to complete the triangle.
Drawing an Equilateral Triangle
Alternative Method Draw lines through points A and B, making angles of 60° with the given line and intersecting C ” rel=”nofollow”>Figure 4.32b).
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How To Construct An Equilateral Triangle Inscribed In A Circle
Suppose you are given a circle, not a side. Suppose you are asked to construct an equilateral triangle inside this circle:
You know only the center point, P , but from that, you can copy the radius .
Create Equilateral Triangle In The Middle Of Canvas
I want to draw an equilateral triangle in the middle of canvas. I tried this:
ctx.moveTo;ctx.lineTo;ctx.lineTo;ctx.fill;
But the triangle looks a bit too tall.
How can I draw an equilateral triangle in the middle of canvas?
Someone told me you have to find the ratio of the height of an equilateral triangle to the side of an equilateral triangle.
h:s
The equation for the three corner points is
x = r*cos + x_centery = r*sin + y_center
where for angle = 0, *, and *; and where r is the radius of the circle in which the triangle is inscribed.
- 2
You have to do it with the height of the triangle
var h = side * /2);
So the ratio h:s is equal to:
sqrt / 2 : 1 = cos : 1 0.866025
- ya or Math.cos or simply 0.866Jan 20 ’12 at 6:39
- 2When I rotate this triangle, it is no longer centred around the original centre. How do I fix this?;user3011902Sep 11 ’15 at 8:53
- Could someone explain why this is needed, and why the example in the question doesn’t work?;ntoonioDec 25 ’17 at 1:46
- @user3011902 I recommend having a look at answer stackoverflow.com/a/8937325 and add an alpha term in both cos and sin: x = r*cos and y = r*sin. You can then change alpha to any value you want, and it will rotate this triangle whilst maintaining its center.
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Properties Of Equilateral Triangle
An equilateral triangle is the one in which all three sides are equal. It is a special case of the isosceles triangle where the third side is also equal. In an equilateral triangle ABC, AB = BC = CA.
Some important properties of an equilateral triangle are:
- An equilateral triangle is a triangle in which all three sides are equal.
- Equilateral triangles also called equiangular. That means, all three internal angles are equal to each other and the only value possible is 60° each.
- It is a regular polygon with 3 sides.
- A triangle is equilateral if and only if the circumcenters of any three of the smaller triangles have the same distance from the centroid.
- A triangle is equilateral if and only if any three of the smaller triangles have either the same perimeter or the same inradius.
- The area of an equilateral triangle is basically the amount of space occupied by an equilateral triangle.
- In an equilateral triangle, the median, angle bisector and perpendicular are all the same and can be simply termed as the perpendicular bisector due to congruence conditions.
- The ortho-centre and centroid of the triangle is the same point.
- In an equilateral triangle, median, angle bisector and altitude for all sides are all the same and are the lines of symmetry of the equilateral triangle.
- The area of an equilateral triangle is 3 a2/ 4
- The perimeter of an equilateral triangle is 3a.
Draw An Equilateral Triangle C#
I have tried to adapt some code I came across to draw an equilateral triangle in c#
public void drawTriangle
Unfortunately, this doesn’t even come close. I have drawn equilateral triangles, but the points were always based on the centers of congruent circles. I am trying to find a simpler way. I am sure there must be an obvious problem with this code, but I am trying to learn the math needed as I go, so I don’t know what it is. Thanks for your time.
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Constructing An Equilateral Triangle Given One Side
How to construct an equilateral triangle given one sideThe theory behind how it worksConstructing an Equilateral Triangle given one side AB;
Proof:
Note:
How To Construct An Equilateral Triangle
Equilateral triangles are easily constructed with a drawing compass, straightedge, and pencil because the 60 ° interior angles can be found using only the radius of a circle around the triangle .
Suppose you are given the length of one side of the required equilateral triangle. You must construct two identical sides that, somehow, create three interior 60
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Area Of Equilateral Triangle
The area of an equilateral triangle is the amount of space that it occupies in a 2-dimensional plane. To recall, an equilateral triangle is a triangle in which all the sides are equal and the measure of all the internal angles is 60°. So, an equilateral triangles area can be calculated if the length of its side is known.
Drawing Triangles In A Loop
from turtle import *drawing_area = Screendrawing_area.setupshapedef draw_triangle: for i in range: forward leftfor i in range: draw_triangle rightdone
from turtle import *drawing_area = Screendrawing_area.setupshapedef draw_triangle: for i in range: forward leftfor i in range: draw_triangle rightdone
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Constructing An Equilateral Triangle Of A Given Side Length Inscribed In A Given Triangle
I am trying to solve the problem of constructing, with straightedge and compass, an equilateral triangle of given side length $a$ inscribed in a given triangle.
I found this post “Inscribe an equilateral triangle inside a triangle” and this other post “How to draw an equilateral triangle inscribed in another triangle?” but the construction must be made with straightedge and compass, using simple constructions such as arcs, parallel lines, perpendicular lines and that kind of thing.
I tried constructing the arcs capable of $120^$ on the sides of the given triangles and noticed that the centers of the arcs form an equilateral triangle, but I don’t know what to do after that.
- ;Calvin LinApr 8 ’20 at 1:39
- $\begingroup$That would be a general equilateral triangle inscribed, not with a given side lenght like is required in my case.$\endgroup$;Lucas FerreiraApr 8 ’20 at 1:50
- $\begingroup$Something is wrong with your question. It seems that for a given triangle there is only one solution when a is not given. If a is different from the side of the equilateral triangle to be inscribed than there is no solution.$\endgroup$Apr 8 ’20 at 4:32
- 1Apr 8 ’20 at 15:14
- $\begingroup$You are right! Will try it now:)$\endgroup$
I believe the following diagrams and incorporated explanation will suffice. Let me know if it is not clear. Click on image to get a larger and clearer view.
$\mathbf.$ Notations, definitions and classifications used in our answer
$\mathbf.$ Construction
How To Draw An Equilateral Triangle In Excel
In addition to the ability to support calculations, Excel also has tools to support users with drawing tools easily.In this article I introduce you How to draw equilateral triangles in Excel 2013.
In addition to the ability to support calculations, Excel also has tools to support users with drawing tools easily.In this article I introduce you How to draw equilateral triangles in Excel 2013 .
Step 1: ;Select the Insert tab -> Shapes -> Flowchart -> Basic Shapes -> ;Select the triangle.
Step 2: Press and hold the Shift key while moving the mouse to customize the size. When it looks like you want to release the mouse button.
With a simple operation you draw an equilateral triangle.
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Deriving Area Of Equilateral Triangle Using Trigonometry
If two sides of a triangle are given, then the height can be calculated using trigonometric functions. Now, the height of a triangle ABC will be-
h = b. Sin C = c. Sin A = a. Sin B
Now, area of ABC = ½ × a × = ½ × b × = ½ × c
Now, since it is an equilateral triangle, A = B = C = 60°
And a = b = c
Area = ½ × a × = ½ × a2 × Sin 60° = ½ × a2 × 3/2
So, Area of Equilateral Triangle = a2
Below is a brief recall about equilateral triangles:
Using An Object With A Circular Base
If you don’t have access to a compass or a protractor, you can use an object with a circular base to trace out an arc instead. This method is essentially the same as using a compass, but you will need to be smart about it!
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How Does Scratch 30 Draw Equilateral Triangles
In scratch 3.0, we can create various geometric shapes by writing, moving, rotating, and repeatedly executing commands. Today, we will take a look at the tutorial of creating equilateral triangles with scratch 3.0.
- Software name:
- Scratch 3.0 offline Edition offline editor v3.6.0 Chinese free installation version
- Software size:
1. Open scratch and enter its main interface;
2. Click events,Add command when green flag is clicked;
3. Click motion,Add move command
4. Change the number of moving steps to 100;
5. AddRotation commandSet the rotation degree to 120;
6. Point
7. Select the brush module;
8. After successfully adding the brush module, find theWriting order
9. Pull the pen down command to the move command;
10. Click control to add repeated execution command and change the number of times to 3 times;
11. Click the green flag to execute the program;
12. The kitten begins to move and records its trajectory,Its exactly an equilateral triangle;
13. Hide the kitten and well see the equilateral triangle created successfully.
Summary:
1. Open scratch 3.0 to enter its main interface;
2. Add brush module;
3. Add move and rotate commands in motion module, and set specific values;
4. Add and repeat the command 3 times.
The above is scratch 3. Create equilateral triangle tutorial, I hope you like it, please continue to pay attention to developeppaer.
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Deriving Area Of Equilateral Triangle Using Rectangle Construction
Consider an equilateral triangle having sides equal to a.
Equilateral Triangle
- Now, draw a straight line from the top vertex of the triangle to the midpoint of the base of the triangle, thus, dividing the base into two equal halves.
Area Of Equilateral Triangle
- Now cut along the straight line and move the other half of the triangle to form the rectangle.
How to find Area of Equilateral Triangle?
Here, the length of the equilateral triangle is considered to be a and the height as h
So the area of an equilateral triangle = Area of a rectangle = ½×a×h .
Half of the rectangle is a right-angled triangle as it can be seen from the figure above.
Thereby, applying the Pythagoras Theorem:
a2;= h2;+; 2
Substituting the value of in , we have:
Area of an Equilateral Triangle
=×a×a
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Constructing An Equilateral Triangle
This page shows how to construct an equilateral trianglewith compass and straightedge or ruler. An equilateral triangle is one with all three sides the same length. It begins with a given line segmentwhich is the length of each side of the desired equilateral triangle.
It works because the compass width is not changed between drawing each side, guaranteeing they are all congruent. It is similar to the 60 degree angle construction, because the interior anglesof an equilateral triangle are all 60 degrees.
Example Questions Using The Equilateral Triangle Area Formula
Question 1: Find the area of an equilateral triangle whose perimeter is 12 cm.
Solution:
Given: Perimeter of an equilateral triangle = 12 cm
As per formula: Perimeter of the equilateral triangle = 3a, where a is the side of the equilateral triangle.
Step 1: Find the side of an equilateral triangle using perimeter.
3a = 12
Thus, the length of side is 4 cm.
Step 2: Find the area of an equilateral triangle using formula.
Area, A = 3 a2/ 4 sq units
= 3 2/ 4;cm2
Therefore, the area of the given equilateral triangle is 43 cm2
Question 2: What is the area of an equilateral triangle whose side is 8;cm?
Solution:
The area of the equilateral triangle = 3 a2/ 4
= 3 × / 4 cm2
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