Area of X Shape given Bottom or Top Angle Calculator

✖Bar Length of X Shape is defined as the length of one bar out of two bars of X Shape.ⓘ Bar Length of X Shape [l_Bar]			+10% -10%
✖Bar Thickness of X Shape is defined as the thickness of one of the bars of X Shape.ⓘ Bar Thickness of X Shape [t_Bar]			+10% -10%
✖The Bottom and Top Angle of X Shape are the bottom-most and top-most angles of the X-Shape formed due to the intersection of two bars forming the X-Shape.ⓘ Bottom and Top Angle of X Shape [∠_Bottom/Top]			+10% -10%

✖The Area of X Shape is defined as the total area enclosed inside the X Shape.ⓘ Area of X Shape given Bottom or Top Angle [A]

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Area of X Shape given Bottom or Top Angle Solution

STEP 0: Pre-Calculation Summary

Formula Used

Area of X Shape = (2*Bar Length of X Shape*Bar Thickness of X Shape*sin(Bottom and Top Angle of X Shape))-((Bar Thickness of X Shape^2)/2*cot(Bottom and Top Angle of X Shape/2))
A = (2*l_Bar*t_Bar*sin(∠_Bottom/Top))-((t_Bar^2)/2*cot(∠_Bottom/Top/2))
This formula uses 2 Functions, 4 Variables

Functions Used

sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)
cot - Cotangent is a trigonometric function that is defined as the ratio of the adjacent side to the opposite side in a right triangle., cot(Angle)

Variables Used

Area of X Shape - (Measured in Square Meter) - The Area of X Shape is defined as the total area enclosed inside the X Shape.
Bar Length of X Shape - (Measured in Meter) - Bar Length of X Shape is defined as the length of one bar out of two bars of X Shape.
Bar Thickness of X Shape - (Measured in Meter) - Bar Thickness of X Shape is defined as the thickness of one of the bars of X Shape.
Bottom and Top Angle of X Shape - (Measured in Radian) - The Bottom and Top Angle of X Shape are the bottom-most and top-most angles of the X-Shape formed due to the intersection of two bars forming the X-Shape.

STEP 1: Convert Input(s) to Base Unit

Bar Length of X Shape: 20 Meter --> 20 Meter No Conversion Required
Bar Thickness of X Shape: 2 Meter --> 2 Meter No Conversion Required
Bottom and Top Angle of X Shape: 45 Degree --> 0.785398163397301 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A = (2*l_Bar*t_Bar*sin(∠_Bottom/Top))-((t_Bar^2)/2*cot(∠_Bottom/Top/2)) --> (2*20*2*sin(0.785398163397301))-((2^2)/2*cot(0.785398163397301/2))

Evaluating ... ...

A = 51.7401153701683

STEP 3: Convert Result to Output's Unit

51.7401153701683 Square Meter --> No Conversion Required

FINAL ANSWER

51.7401153701683 ≈ 51.74012 Square Meter <-- Area of X Shape

(Calculation completed in 00.004 seconds)

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Created by Devendar Kachhwaha

Indian Institute of technology (IIT-BHU), Varanasi

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< Area of X Shape Calculators

Area of X Shape given Left or Right Angle

LaTeX Go Area of X Shape = (2*Bar Length of X Shape*Bar Thickness of X Shape*sin(Left and Right Angle of X Shape))-(Bar Thickness of X Shape*sin(Left and Right Angle of X Shape/2))^2/sin(Left and Right Angle of X Shape)

Area of X Shape given Bottom or Top Angle

LaTeX Go Area of X Shape = (2*Bar Length of X Shape*Bar Thickness of X Shape*sin(Bottom and Top Angle of X Shape))-((Bar Thickness of X Shape^2)/2*cot(Bottom and Top Angle of X Shape/2))

Area of X Shape given Bottom or Top Angle Formula

LaTeX Go

What is X Shape?

When a parallelogram shaped bar is reflected and connected with the original bar in the center then the formed shape is known as X shape. The intersection of both bars is a rhombus of which side length is called crossing length.

How to Calculate Area of X Shape given Bottom or Top Angle?

Area of X Shape given Bottom or Top Angle calculator uses Area of X Shape = (2*Bar Length of X Shape*Bar Thickness of X Shape*sin(Bottom and Top Angle of X Shape))-((Bar Thickness of X Shape^2)/2*cot(Bottom and Top Angle of X Shape/2)) to calculate the Area of X Shape, The Area of X Shape given Bottom or Top Angle is defined as the total space occupied by the X Shape in 2D space. Area of X Shape is denoted by A symbol.

How to calculate Area of X Shape given Bottom or Top Angle using this online calculator? To use this online calculator for Area of X Shape given Bottom or Top Angle, enter Bar Length of X Shape (l_Bar), Bar Thickness of X Shape (t_Bar) & Bottom and Top Angle of X Shape (∠_Bottom/Top) and hit the calculate button. Here is how the Area of X Shape given Bottom or Top Angle calculation can be explained with given input values -> 51.74012 = (2*20*2*sin(0.785398163397301))-((2^2)/2*cot(0.785398163397301/2)).

FAQ

What is Area of X Shape given Bottom or Top Angle?

The Area of X Shape given Bottom or Top Angle is defined as the total space occupied by the X Shape in 2D space and is represented as A = (2*l_Bar*t_Bar*sin(∠_Bottom/Top))-((t_Bar^2)/2*cot(∠_Bottom/Top/2)) or Area of X Shape = (2*Bar Length of X Shape*Bar Thickness of X Shape*sin(Bottom and Top Angle of X Shape))-((Bar Thickness of X Shape^2)/2*cot(Bottom and Top Angle of X Shape/2)). Bar Length of X Shape is defined as the length of one bar out of two bars of X Shape, Bar Thickness of X Shape is defined as the thickness of one of the bars of X Shape & The Bottom and Top Angle of X Shape are the bottom-most and top-most angles of the X-Shape formed due to the intersection of two bars forming the X-Shape.

How to calculate Area of X Shape given Bottom or Top Angle?

The Area of X Shape given Bottom or Top Angle is defined as the total space occupied by the X Shape in 2D space is calculated using Area of X Shape = (2*Bar Length of X Shape*Bar Thickness of X Shape*sin(Bottom and Top Angle of X Shape))-((Bar Thickness of X Shape^2)/2*cot(Bottom and Top Angle of X Shape/2)). To calculate Area of X Shape given Bottom or Top Angle, you need Bar Length of X Shape (l_Bar), Bar Thickness of X Shape (t_Bar) & Bottom and Top Angle of X Shape (∠_Bottom/Top). With our tool, you need to enter the respective value for Bar Length of X Shape, Bar Thickness of X Shape & Bottom and Top Angle of X Shape 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 Area of X Shape?

In this formula, Area of X Shape uses Bar Length of X Shape, Bar Thickness of X Shape & Bottom and Top Angle of X Shape. We can use 1 other way(s) to calculate the same, which is/are as follows -

Area of X Shape = (2*Bar Length of X Shape*Bar Thickness of X Shape*sin(Left and Right Angle of X Shape))-(Bar Thickness of X Shape*sin(Left and Right Angle of X Shape/2))^2/sin(Left and Right Angle of X Shape)

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