Table of Contents
How many sides does a polygon with 54 diagonals have?
12
So, the number of sides of a polygon which have 54 diagonals is 12.
What is the formula to find diagonal of a polygon?
Formula Method: According to the formula, number of diagonals = n (n-3)/ 2. So, 11-sided polygon will contain 11(11-3)/2 = 44 diagonals.
How many diagonals does a 45 sided polygon have?
Each vertex makes a diagonal with n-3 other vertices – as discussed before. So, each vertex will make 15 diagonals. Since 3 vertices are not counted, they will not send out each of these 15 diagonals i.e. 45 diagonals. But in this figure of 45, we have double counted 3 diagonals.
How many sides has a polygon if the sum of its angles is 44 right angles?
A rectangle has 4 sides, so the sum of the angles is 360. Pretty easy to see, as all 4 angles are 90. 44 right angles sums up to 44*90 = 22*180 = (24–2)*180. So the polygon has 24 sides.
How many sides does a polygon have with 230 diagonals?
Therefore, a quadrilateral has two diagonals, joining opposite pairs of vertices. For any convex polygon, all the diagonals are inside the polygon, but for re-entrant polygons, some diagonals are outside of the polygon….Polygons.
Sides | Diagonals |
---|---|
20 | 170 |
21 | 189 |
22 | 209 |
23 | 230 |
How many sides does a polygon have with 170 diagonals?
Another way to express the general rule for the total number of diagonals is to think about the number of diagonals that can be drawn from each vertex in a polygon. That is “3” less than the number of sides. Therefore, for a 20-sided polygon, there will be 190 lines and 170 diagonals.
How many diagonals does a polygon with 22 sides have?
209 diagonals
So, a polygon with 22 sides has 209 diagonals.
How many diagonals are in a 40 sided polygon?
740
Polygons
Sides | Diagonals |
---|---|
39 | 702 |
40 | 740 |
41 | 779 |
42 | 819 |
How many diagonals are in a 20 sided polygon?
170 diagonals
Therefore, for a 20-sided polygon, there will be 190 lines and 170 diagonals.
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