Diameter of Fourstar given Edge Length and Inner Angle Calculator

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✖The Edge Length of Fourstar is the length of any edge of the Fourstar shape from one end to other end.ⓘ Edge Length of Fourstar [l_e]			+10% -10%
✖The Inner Angle of Fourstar is the unequal angle of the isosceles triangle that attached to the square or the angle between the edges which form the triangular spike, of the Fourstar.ⓘ Inner Angle of Fourstar [∠_Inner]			+10% -10%

✖The Diameter of Fourstar is the distance between the opposite spike tips of the Fourstar.ⓘ Diameter of Fourstar given Edge Length and Inner Angle [D]

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Formula

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Diameter of Fourstar given Edge Length and Inner Angle

Formula

`"D" = "l"_{"e"}*sqrt(2)*(sqrt(1+cos("∠"_{"Inner"}))+sqrt(1-cos("∠"_{"Inner"})))`

Example

`"14.02115m"="5m"*sqrt(2)*(sqrt(1+cos("75°"))+sqrt(1-cos("75°")))`

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Diameter of Fourstar given Edge Length and Inner Angle Solution

STEP 0: Pre-Calculation Summary

Formula Used

Diameter of Fourstar = Edge Length of Fourstar*sqrt(2)*(sqrt(1+cos(Inner Angle of Fourstar))+sqrt(1-cos(Inner Angle of Fourstar)))
D = l_e*sqrt(2)*(sqrt(1+cos(∠_Inner))+sqrt(1-cos(∠_Inner)))
This formula uses 2 Functions, 3 Variables

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Diameter of Fourstar - (Measured in Meter) - The Diameter of Fourstar is the distance between the opposite spike tips of the Fourstar.
Edge Length of Fourstar - (Measured in Meter) - The Edge Length of Fourstar is the length of any edge of the Fourstar shape from one end to other end.
Inner Angle of Fourstar - (Measured in Radian) - The Inner Angle of Fourstar is the unequal angle of the isosceles triangle that attached to the square or the angle between the edges which form the triangular spike, of the Fourstar.

STEP 1: Convert Input(s) to Base Unit

Edge Length of Fourstar: 5 Meter --> 5 Meter No Conversion Required
Inner Angle of Fourstar: 75 Degree --> 1.3089969389955 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

D = l_e*sqrt(2)*(sqrt(1+cos(∠_Inner))+sqrt(1-cos(∠_Inner))) --> 5*sqrt(2)*(sqrt(1+cos(1.3089969389955))+sqrt(1-cos(1.3089969389955)))

Evaluating ... ...

D = 14.0211476929993

STEP 3: Convert Result to Output's Unit

14.0211476929993 Meter --> No Conversion Required

FINAL ANSWER

14.0211476929993 ≈ 14.02115 Meter <-- Diameter of Fourstar

(Calculation completed in 00.004 seconds)

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< 10+ Fourstar Calculators

Diameter of Fourstar given Edge Length and Inner Angle

Go Diameter of Fourstar = Edge Length of Fourstar*sqrt(2)*(sqrt(1+cos(Inner Angle of Fourstar))+sqrt(1-cos(Inner Angle of Fourstar)))

Spike Height of Fourstar given Inner Angle

Go Spike Height of Fourstar = Edge Length of Fourstar/2*sqrt(2*(1+cos(Inner Angle of Fourstar)))

Chord Length of Fourstar

Go Chord Length of Fourstar = sqrt(2*Edge Length of Fourstar^2*(1-cos(Outer Angle of Fourstar)))

Spike Base of Fourstar

Go Spike Base of Fourstar = sqrt(2*Edge Length of Fourstar^2*(1-cos(Inner Angle of Fourstar)))

Area of Fourstar

Go Area of Fourstar = (2*Spike Height of Fourstar*Spike Base of Fourstar)+Spike Base of Fourstar^2

Spike Height of Fourstar

Go Spike Height of Fourstar = sqrt((4*Edge Length of Fourstar^2-Spike Base of Fourstar^2)/4)

Spike Base of Fourstar given Diameter

Go Spike Base of Fourstar = Diameter of Fourstar-2*Spike Height of Fourstar

Diameter of Fourstar

Go Diameter of Fourstar = 2*Spike Height of Fourstar+Spike Base of Fourstar

Outer Angle of Fourstar

Go Outer Angle of Fourstar = Inner Angle of Fourstar+pi/2

Perimeter of Fourstar

Go Perimeter of Fourstar = 8*Edge Length of Fourstar

Diameter of Fourstar given Edge Length and Inner Angle Formula

Diameter of Fourstar = Edge Length of Fourstar*sqrt(2)*(sqrt(1+cos(Inner Angle of Fourstar))+sqrt(1-cos(Inner Angle of Fourstar)))
D = l_e*sqrt(2)*(sqrt(1+cos(∠_Inner))+sqrt(1-cos(∠_Inner)))

What is a Fourstar?

Fourstar is basically a four petal star shape. More clearly, it consists of a square and four identical triangles each having one side equal to the side length of the square. Each triangle is joined to the square with side of triangle with same length as the square coincide each other.

How to Calculate Diameter of Fourstar given Edge Length and Inner Angle?

Diameter of Fourstar given Edge Length and Inner Angle calculator uses Diameter of Fourstar = Edge Length of Fourstar*sqrt(2)*(sqrt(1+cos(Inner Angle of Fourstar))+sqrt(1-cos(Inner Angle of Fourstar))) to calculate the Diameter of Fourstar, The Diameter of Fourstar given Edge Length and Inner Angle formula is defined as the distance between the sharp tips of any two opposite triangular petals of a Fourstar, calculated using edge length and inner angle. Diameter of Fourstar is denoted by D symbol.

How to calculate Diameter of Fourstar given Edge Length and Inner Angle using this online calculator? To use this online calculator for Diameter of Fourstar given Edge Length and Inner Angle, enter Edge Length of Fourstar (l_e) & Inner Angle of Fourstar (∠_Inner) and hit the calculate button. Here is how the Diameter of Fourstar given Edge Length and Inner Angle calculation can be explained with given input values -> 14.02115 = 5*sqrt(2)*(sqrt(1+cos(1.3089969389955))+sqrt(1-cos(1.3089969389955))).

FAQ

What is Diameter of Fourstar given Edge Length and Inner Angle?

The Diameter of Fourstar given Edge Length and Inner Angle formula is defined as the distance between the sharp tips of any two opposite triangular petals of a Fourstar, calculated using edge length and inner angle and is represented as D = l_e*sqrt(2)*(sqrt(1+cos(∠_Inner))+sqrt(1-cos(∠_Inner))) or Diameter of Fourstar = Edge Length of Fourstar*sqrt(2)*(sqrt(1+cos(Inner Angle of Fourstar))+sqrt(1-cos(Inner Angle of Fourstar))). The Edge Length of Fourstar is the length of any edge of the Fourstar shape from one end to other end & The Inner Angle of Fourstar is the unequal angle of the isosceles triangle that attached to the square or the angle between the edges which form the triangular spike, of the Fourstar.

How to calculate Diameter of Fourstar given Edge Length and Inner Angle?

The Diameter of Fourstar given Edge Length and Inner Angle formula is defined as the distance between the sharp tips of any two opposite triangular petals of a Fourstar, calculated using edge length and inner angle is calculated using Diameter of Fourstar = Edge Length of Fourstar*sqrt(2)*(sqrt(1+cos(Inner Angle of Fourstar))+sqrt(1-cos(Inner Angle of Fourstar))). To calculate Diameter of Fourstar given Edge Length and Inner Angle, you need Edge Length of Fourstar (l_e) & Inner Angle of Fourstar (∠_Inner). With our tool, you need to enter the respective value for Edge Length of Fourstar & Inner Angle of Fourstar and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Diameter of Fourstar?

In this formula, Diameter of Fourstar uses Edge Length of Fourstar & Inner Angle of Fourstar. We can use 1 other way(s) to calculate the same, which is/are as follows -

Diameter of Fourstar = 2*Spike Height of Fourstar+Spike Base of Fourstar

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