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How do you find the perimeter of an octagon if you know the diameter?
Wiki User
∙ 9y ago
I presume by diameter of an octagon you mean the length of the diagonal between opposite vertices of a regular octagon.
By completing all the diagonals between opposite vertices of a regular octagon, it divides it up into 8 equal isosceles triangles, with their apexes at the centre of the octagon. The two sides of these isosceles triangles which go from a vertex of the octagon to the centre has a length half that of the diameter.
If the centre point of each side of the octagon is joined to the centre of the octagon, each of the 8 isosceles triangles above are split into two (congruent) right angled triangles. The angle at the centre of the octagon of each of these triangles is (360° ÷ 8) ÷ 2 = 22.5°.
The side opposite this angle is half the length of the side of the octagon and so the perimeter is 16 times its length.
The hypotenuse of the right angled triangles is half the diameter. Thus the trigonometric sine function can be used to find half the octagons side length, and thus its perimeter:
sin = opp/hyp
→ opp = sin x hyp
Perimeter = 16 x opp = 16 x (sin 22.5° x diameter/2) = diameter x 8 x sin 22.5° ≈ diameter x 3.061
This can be generalised to any regular even sided polygon if diameter is defined as the length of the diagonal between opposite vertices (which is also the maximum straight line distance between two points on the perimeter):
perimeter = diameter x number_of_sides x sin(180° ÷ number_of_sides)
As the number of sides increases, "number_of_sides x sin(180° ÷ number_of_sides)" gets closer and closer to π.
Wiki User
∙ 9y ago
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How do you find the radius of a circle if you know the perimeter?
you can divide the perimeter(circumference) by pi(3.14) and then once you get your answer you divide that by two giving you the length of the radius of the circle. ex: perimeter = 34pi 34pi/pi 34/2=diameter 16=radius
Is it true that you can't find the perimeter if you don't know the area?
Not exactly. If I know the side lengths, I can still find the perimeter
How do you find the perimeter of two concentric circles?
The perimeter of a circle is the same as it's circumference. To find this, you will need to know it's radius or diameter.For example, if the diameter of a circle is 7, you could do: pi times the diameter (which is 7), or, if you want to, you could half it and have; 2 times pi times 3.5. It doesn't matter which way you have it, you will still get the same answer if it is halved correctly.
When do you need to find perimeter?
You need to find perimeter when you buy a house, because then you know where your yard begins and ends.
How do you find the area of an octagon when you only know the apothegm?
ask. mrs.cwiklinski
How do you find the circumference of a circle if only the perimeter is given?
The perimeter of a circle is the circumference. If you mean the circle is drawn around (and touches the 4 corners of) a square, and you know the perimeter of the square, you divide the square's perimeter by 4, do pythagorean's theorem on the 2 sides (legs) to find the hypotenuse, and that hypotenuse will be the diameter of the circle. You then multiply that diameter you get by pi to get the circumference.
How do you find the perimeter of a triangle when the perimeter is 177?
If you know the perimeter, there is no need to find it again.
How do you find the radius of a circle if you know the perimeter?
you can divide the perimeter(circumference) by pi(3.14) and then once you get your answer you divide that by two giving you the length of the radius of the circle. ex: perimeter = 34pi 34pi/pi 34/2=diameter 16=radius
What is the outside of a 3D shape called I know perimeter is for 2D shapes?
Diameter
How do you draw an octagon on a circle that has a diameter of 8cm?
i don't know i think you should just try your best
Is it true that you can't find the perimeter if you don't know the area?
Not exactly. If I know the side lengths, I can still find the perimeter
What is the perimeter of a regular pentagon with a side length of 7.2 cm?
we know that regular pentagon has 5 equilateral triangle . now ,perimeter of pentagon = 5 Xside . now,perimeter of a regular pentagon with a side length of 7.2 cm . perimeter = 7.2 X 5 =36 cm .
How do you algebraically determine the perimeterof arectangular octagon inscribed in a circle of diameter 15cmEach side of the octagon is 6.9cm from the centre of the circle?
We know that an octagon is an eight-side polygon. Since each side has the same distance form the center of the circumscribed circle of the octagon, this octagon is a regular octagon. If we draw the radii of the circle (their endpoints there are at the vertexes of the octagon), we form 8 isosceles triangle, which radius represents two their congruent sides with a measure of 7.5 cm, and the distance drawn from the center of the circle to the sides of the octagon represents their altitudes with a measure of 6.9 cm. So, by using the Pythagorean theorem we can find the half of the side of the octagon, which is: 7.5)^2 - (6.9)^2 = 8.64 Since one half of the octagon side is square root of 8.64, the whole side is 2(square root of 8.64) Thus the perimeter of this octagon is approximately 47 cm [8 x 2(square root of 8.64)].
How do you find the perimeter of two concentric circles?
The perimeter of a circle is the same as it's circumference. To find this, you will need to know it's radius or diameter.For example, if the diameter of a circle is 7, you could do: pi times the diameter (which is 7), or, if you want to, you could half it and have; 2 times pi times 3.5. It doesn't matter which way you have it, you will still get the same answer if it is halved correctly.
If you know the perimeter how do you find length?
there is no way because you have to add the sides to get the perimeter.
How do you find the area if you know the perimeter?
It is impossible
Can you find the height of a triangle when you know the perimeter?
No.
