What is the ratio of longest diagonal to the shortest diagonal in a regular octagon an eight sided polygon )?

Hence, the answer is √2 : 1.

What is the longest diagonal of an octagon?

In total, an octagon has 20 diagonals; the longest ones are on its axes of symmetry, and they meet at the central point, O, which is also the origin of symmetry….Here are the formulas for the length of the diagonals:

• Short diagonal s = a * √(2 + √2)
• Medium diagonal m = a * (1 + √2)
• Long diagonal l = a * √(4 + 2√2)

How do you find the diagonal of a octagon?

Octagon Diagonals In this case, there are 8 sides in an octagon. After substituting the value of ‘n’ in the formula, we get, Number of diagonals = n(n-3)/2 = 8(8 – 3)/2 = (8 × 5)/2 = 20.

What is the formula for finding the longest diagonal?

6/ The line DY divides triangle ABD in half, so the angle ADY is a/2, and the length AY = half AD = L/2. The line DA is d, the longest diagonal which is what we’ve been trying to work out all this time, remember? EQUATION IV: sin(a/2) = (L/2)/d.

How do you find the shortest diagonal of a hexagon?

Method of solving this CAT Question from Regular Hexagon: A regular hexagon is just 6 equilateral triangles around a point. Let side of regular hexagon be a. The shortest diagonal will be of length a√3.

What is the length of diagonal of hexagon?

Explanation: Regular hexagons are comprised of six equilateral triangles; in our question, these triangles each have side length 4 (see diagram). The length of a diagonal is equal to two times the length of the side. In this instance, the answer is 8.

How many diagonals are in octagon?

20 diagonals
∴ The octagon has 20 diagonals. Hence, option C is the correct answer. Note: The octagon is a polygon in geometry, which has 8 sides and 8 angles.

How do you find the longest diagonal of a hexagon?

Correct answer: The hexagon can be broken down into 6 equilateral triangles. Each side of the equilateral triangle is equal. Two of the combined lengths of the equilateral triangles join to form the diagonal of the hexagon. Therefore, the diagonal is twice the side length of the hexagon.

How do you find the long diagonal of a hexagon?

To find the diagonals of hexagons, use the formula: n (n-3)/2, where n is the number of sides of a polygon. For a hexagon, n = 6, and 6 (6-3) / 2 equals nine diagonals.

Which is the longest and shortest diagonal of an octagon?

AE is the longest and AC is the shortest diagonal. Let AB=BC=s, the side of the octagon. Let us consider the portion ABCDE of a regular octagon. AE is the longest and AC is the shortest diagonal. Let AB=BC=s, the side of the octagon.

What is the length of the diagonal of a hexagon?

Regular hexagons are comprised of six equilateral triangles; in our question, these triangles each have side length 4 (see diagram). The length of a diagonal is equal to two times the length of the side.

Which side of the Octagon is a right angled triangle?

AE is the longest and AC is the shortest diagonal. Let AB=BC=s, the side of the octagon. ⎳ADE = 135º-45º = 90º. Therefore it is a right angled triangle. Please upvote if you find this useful !

How many diagonals does a pentagon have?

The formula for the number of diagonals of a polygon is: where n = the number of sides in the polygon. Thus a pentagon thas 5 diagonals. An octagon has 20 diagonals. Kean University, Bachelors, Mathematics.