Exactly 10 of those are sides of the decagon, the others are diagonals. Answer: Corrected ; original had "10 choose 9" for no reason other than my lack of concentration. Ans :. Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. How many diagonals does a decagon have?
Ask Question. Asked 5 years, 5 months ago. Active 4 years, 7 months ago. Viewed 31k times. Taussig Draw diagonals in different colors to make them easier to count. Note that this method gets much more difficult with polygons that have more than ten sides.
Count the diagonals. There are two options for counting: you can count as you draw the diagonals or count them once they have been drawn. As you count each diagonal, draw a small number above the diagonal to denote that it has been counted. It is easy to lose track while counting when there are a lot of diagonals crossing each other. For the square, there are two diagonals: one diagonal for every two vertices. A hexagon has 9 diagonals: there are three diagonals for every three vertices.
An octagon has 20 diagonals. Past the heptagon, it gets more difficult to count the diagonals because there are so many of them. Beware of counting a diagonal more than once. Take care when counting the diagonals to count each one only once. Each vertex has two diagonals, so if you counted each diagonal from every vertex twice, you might think there were 10 diagonals. This is incorrect because you would have counted each diagonal twice! Practice with some examples. Draw some other polygons and count the number of diagonals.
The polygon does not have to be symmetric for this method to work. In the case of a concave polygon, you may have to draw some of the diagonals outside the actual polygon.
A octagon has 20 diagonals. Method 2. Define the formula. You may see it either way, both equations are identical. This equation can be used to find the number of diagonals of any polygon. Note that the triangle is an exception to this rule. Due to the shape of the triangle, it does not have any diagonals. Identify the number of sides in the polygon. To use this formula, you must identify the number of sides that the polygon has.
The number of sides is given in the name of the polygon, you just need to know what each name means. Here are some of common prefixes you will see in polygons: [10] X Research source Tetra 4 , penta 5 , hexa 6 , hepta 7 , octa 8 , ennea 9 , deca 10 , hendeca 11 , dodeca 12 , trideca 13 , tetradeca 14 , pentadeca 15 , etc. For example, a sided polygon would be written as gon.
If you are given a picture of the polygon, you can simply count the number of sides. Plug the number of sides into the equation. Once you know how many sides the polygon has, you just need to plug that number into the equation and solve.
Solve the equation. Finish by solving the equation using the proper order of operations. Start by solving the subtraction, then multiply, then divide.
The final answer is the number of diagonals the polygon has. Practice with more examples. The more practice you have with a math concept, the better you will be at using it. Doing lots of examples will also help you memorize the formula in case you need it for a quiz, test, or exam. Remember, this formula works for a polygon of any number of sides greater than 3.
Did you know you can get expert answers for this article? Unlock expert answers by supporting wikiHow. Jake Adams. While complex decagons refer to decagons that are self-intersecting and have additional interior spaces. They do not strictly follow any prescribed rules of decagons regarding their interior angles and their sums.
To find the sum of the interior angles of a decagon, first, divide it into triangles. There are eight triangles in a regular decagon. We know that the number of sides of a decagon is To find the measure of the central angle of a regular decagon, we need to draw a circle in the middle. Divide this by ten, because a decagon has 10 sides.
A diagonal is a line that can be drawn from one vertex to another. By joining one vertex to the remaining vertices of the decagon, 8 triangles will be formed. Look at the image given below, showing diagonals and triangles of a decagon. Like other shapes, a regular decagon also has the formula to calculate perimeter and area.
The formulas are mentioned below:. In the case of an irregular decagon, we can simply add the side lengths to find the perimeter. Example 1 : Jenifer's hobby is collecting coins from various countries.
She found a new coin to add to her collection. Find out whether this coin resembles a decagon shape or not? Solution: Decagon has ten sides and ten angles. Therefore, the coin is not in a decagon shape as it only has 7 sides. A decagon can be recognized as a polygon with 10 sides, 10 interior angles, and 10 vertices.
Decagon can be regular and irregular. Regular decagon has all equal sides. Irregular decagon has unequal sides. If we know the measurement of the side length of a regular decagon, then we can use this formula to find the area. There is no formula to find the area of an irregular decagon, but we can divide it into triangles and try to find the area of all triangles and add them.
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