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How many diagonals does a shape with 8 sides have?
The formula for determining the number of diagonals in a shape is n(n-3)/2 where n=vertices, (corners or intersections of geometric shapes). For an eight sided shape we replace n with 8. 8(8-3)/2 8(5)/2 (8x5)/2 40/2=20 An octagon contains 20 diagonals. For a further example we can determine the diagonals in a shape with 5 sides: 5(5-3)/2 5(2)/2 (5x2)/2 10/2=5 A Pentagon contains 5 diagonals.
What is the largest number of diagonals that can be drawn inside a polygon with n sides?
Formula: number of diagonals = 1/2 * n(n-3) where n is the number of sides or vertices Example: to get the number of diagonals in a pentagon pentagon has 5 sides or vertices; thus, n = 5 no. of diagonals: = 1/2 * n(n-3) = 1/2 * 5(5-3) = 1/2 * 5(2) = 1/2 * 10 = 10/2 = 5
How many diagonals in pentagon have?
It has 5 diagonals.Formula: number of distinct diagonals = n(n-3)/2where n is the number of sides (or vertices)number of diagonals in pentagon:= 5(5-3)/2= 5(2)/2= 10/2= 5Answer: There are 5 diagonals in pentagon.
What is the name of the the polygon with 5 diagonals?
The polygon with 5 diagonals is a heptagon. A heptagon has seven sides, and the formula for calculating the number of diagonals in a polygon is given by ( \frac{n(n-3)}{2} ), where ( n ) is the number of sides. For a heptagon, substituting ( n = 7 ) yields ( \frac{7(7-3)}{2} = 5 ) diagonals.
What are the mathematical names of the first ten polygons and their properties?
All polygons have 3 or more sides having exterior angles that add up to 360 degrees and the first 10 can be classed as follows in order of their geometrical names, number of sides, sum of interior angles and number of diagonals:- 1 Triangle: 3 sides, 180 degrees and no diagonals 2 Quadrilateral: 4 sides, 360 degrees and 2 diagonals 3 Pentagon: 5 sides, 540 degrees and 5 diagonals 4 Hexagon: 6 sides, 720 degrees and 9 diagonals 5 Heptagon or Septagon: 7 sides, 900 degrees and 14 diagonals 6 Octagon: 8 sides, 1080 degrees and 20 diagonals 7 Nonagon: 9 sides, 1260 degrees and 27 diagonals 8 Decagon: 10 sides, 1440 degrees and 35 diagonals 9 Undecagon: 11 sides, 1620 degrees and 44 diagonals 10 Dodecagon: 12 sides, 1800 degrees and 54 diagonals Note that all polygons can be regular, irregular, congruent or similar
How many diagonals does a shape with 5 sides have?
5(5-3)/2. That it is the formula so that shape would have 5 diagonals. n(n-3)/2 where n is the number of sides
How many diagonals does a shape with 8 sides have?
The formula for determining the number of diagonals in a shape is n(n-3)/2 where n=vertices, (corners or intersections of geometric shapes). For an eight sided shape we replace n with 8. 8(8-3)/2 8(5)/2 (8x5)/2 40/2=20 An octagon contains 20 diagonals. For a further example we can determine the diagonals in a shape with 5 sides: 5(5-3)/2 5(2)/2 (5x2)/2 10/2=5 A Pentagon contains 5 diagonals.
What is the largest number of diagonals that can be drawn inside a polygon with n sides?
Formula: number of diagonals = 1/2 * n(n-3) where n is the number of sides or vertices Example: to get the number of diagonals in a pentagon pentagon has 5 sides or vertices; thus, n = 5 no. of diagonals: = 1/2 * n(n-3) = 1/2 * 5(5-3) = 1/2 * 5(2) = 1/2 * 10 = 10/2 = 5
How many diagonals in pentagon have?
It has 5 diagonals.Formula: number of distinct diagonals = n(n-3)/2where n is the number of sides (or vertices)number of diagonals in pentagon:= 5(5-3)/2= 5(2)/2= 10/2= 5Answer: There are 5 diagonals in pentagon.
What is the name of the the polygon with 5 diagonals?
The polygon with 5 diagonals is a heptagon. A heptagon has seven sides, and the formula for calculating the number of diagonals in a polygon is given by ( \frac{n(n-3)}{2} ), where ( n ) is the number of sides. For a heptagon, substituting ( n = 7 ) yields ( \frac{7(7-3)}{2} = 5 ) diagonals.
How many triangles are formed by drawing diagonals from one vertex of a polygon with fifty sides?
use the formula s-2 (s=sides) there are 2 triangles in a square, which has 4 sides:4-2=2 there are 3 triangles in a pentagon, which has 5 sides:5-2=3 so, there should be 48 triangles in a shape with 50 sides:50-2=48
How many diagonals are in a 7 sided polygon?
A 4-sided polygon has 2 diagonals. A 5-sided polygon, 5. 6-sided, 9. By induction, an n-sided polygon has 'n*(n-3)/2' diagonals. "n" is how many sides a shape has. so, (7)*(7-3)/2 now we have, 7*4/2 so, 28/2 = 14 Therefore, a 7-sided polygon would have 14 diagonals.
What are the mathematical names of the first ten polygons and their properties?
All polygons have 3 or more sides having exterior angles that add up to 360 degrees and the first 10 can be classed as follows in order of their geometrical names, number of sides, sum of interior angles and number of diagonals:- 1 Triangle: 3 sides, 180 degrees and no diagonals 2 Quadrilateral: 4 sides, 360 degrees and 2 diagonals 3 Pentagon: 5 sides, 540 degrees and 5 diagonals 4 Hexagon: 6 sides, 720 degrees and 9 diagonals 5 Heptagon or Septagon: 7 sides, 900 degrees and 14 diagonals 6 Octagon: 8 sides, 1080 degrees and 20 diagonals 7 Nonagon: 9 sides, 1260 degrees and 27 diagonals 8 Decagon: 10 sides, 1440 degrees and 35 diagonals 9 Undecagon: 11 sides, 1620 degrees and 44 diagonals 10 Dodecagon: 12 sides, 1800 degrees and 54 diagonals Note that all polygons can be regular, irregular, congruent or similar
What has 5 sides and 5 diagonals?
It is a 5 sided pentagon
What is the number of diagonals drawn from one vertex on a heptagon?
a heptagon has 7 sides. you cannot draw a diagonal to the 2 adjacent vertices, so 7-2 = 5. there would be 5 diagonals.
Does a polygon ever have more diagonals than sides?
The number of diagonals for a shape with x sides is (x²-3x)/2 The number of sides is x You want to know if x is ever less than (x²-3x)/2 or else (x²-3x)/2 - x > 0 (x² - 3x) / 2 - x > 0 (x² - 3x)/2 - (2x)/x > 0 x² - 3x - 2x > 0 x² - 5x > 0 x(x-5)>0 This only true if x<0 or x>5, and since a polygon cannot have less than 2 sides, x<0 is meaningless. This means that if x<5 then the number of diagonals is less than the number of sides, equal for x=5, and more for x>5. ■
What polygon has the same number of diagonals as it has sides?
In short: The Pentagon In Long: The formula for the number of diagonals is (x*(x-3))/2 So if you make that equal to x you get 5. (x(x-3))/2=x (x^2-3x)/2=x x^2-3x=2x x^2-5x=0 x=0 or x-5=0 x=0 or x=5 x=5 Because there is no polygon with 0 sides and the pentagon is defined as a polygon with 5 sides, the pentagon is the only regular polygon with the same amount of diagonals as it has sides.
