Area of X Shape given bottom angle Calculator

Main Category	Math ↺
Math	Geometry ↺
Geometry	2D Geometry ↺
2D Geometry	X Shape ↺

✖Length is the measurement or extent of something from end to end.ⓘ Length [L]			+10% -10%
✖Thickness is the distance through an object.ⓘ Thickness [t]			+10% -10%
✖The bottom angle is the bottom most angle of the given geometry.ⓘ Bottom angle [Angle_Bottom]			+10% -10%

✖The area is the amount of two-dimensional space taken up by an object.ⓘ Area of X Shape given bottom angle [A]

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Credits

Devendar Kachhwaha

Indian Institute of technology (IIT-BHU), Varanasi

Devendar Kachhwaha has created this Calculator and 25+ more calculators!

Jaseem K

IIT Madras (IIT Madras), Chennai

Jaseem K has verified this Calculator and 50+ more calculators!

Area of X Shape given bottom angle Solution

STEP 0: Pre-Calculation Summary

Formula Used

Area = (2*Length*Thickness*sin(Bottom angle))-((((Thickness)^2)*cot(Bottom angle/2))/2)
A = (2*L*t*sin(Angle_Bottom))-((((t)^2)*cot(Angle_Bottom/2))/2)
This formula uses 2 Functions, 3 Variables

Functions Used

sin - Trigonometric sine function, sin(Angle)
cot - Trigonometric cotangent function, cot(Angle)

Variables Used

Length - Length is the measurement or extent of something from end to end. (Measured in Meter)
Thickness - Thickness is the distance through an object. (Measured in Meter)
Bottom angle - The bottom angle is the bottom most angle of the given geometry. (Measured in Radian)

STEP 1: Convert Input(s) to Base Unit

Length: 3 Meter --> 3 Meter No Conversion Required
Thickness: 1 Meter --> 1 Meter No Conversion Required
Bottom angle: 0.528 Radian --> 0.528 Radian No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A = (2*L*t*sin(Angle_Bottom))-((((t)^2)*cot(Angle_Bottom/2))/2) --> (2*3*1*sin(0.528))-((((1)^2)*cot(0.528/2))/2)

Evaluating ... ...

A = 1.1731067170978

STEP 3: Convert Result to Output's Unit

1.1731067170978 Square Meter --> No Conversion Required

FINAL ANSWER

1.1731067170978 Square Meter <-- Area

(Calculation completed in 00.016 seconds)

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< 10+ X Shape Calculators

Perimeter of X Shape

Perimeter = 4*(Thickness+Length-Thickness*sin(pi/2-atan(Width/Height))/sin(pi-2*atan(Width/Height))) Go

Inner arm length of X Shape

Inner arm length = Length/2-Thickness*sin(pi/2-atan(Width/Height))/sin(pi-2*atan(Width/Height)) Go

Crossing length of X Shape

Crossing Length = Thickness*sin(pi/2-atan(Width/Height))/sin(pi-2*atan(Width/Height)) Go

Area of X Shape given crossing length

Area = (2*Length*Thickness*sin(Top angle))-(((Crossing Length)^2)*sin(Top angle)) Go

Crossing length of X Shape given top angle

Crossing Length = (Thickness/2)*cosec(Top angle/2) Go

Bottom angle of X Shape

Bottom angle = 2*atan(Width/Height) Go

Right angle of X Shape

Right angle = 2*atan(Height/Width) Go

Left angle of X Shape

Left angle = 2*atan(Height/Width) Go

Top angle of X Shape

Top angle = 2*atan(Width/Height) Go

Outer arm length of X Shape

Outer Arm Length = Length/2 Go

Area of X Shape given bottom angle Formula

Area = (2*Length*Thickness*sin(Bottom angle))-((((Thickness)^2)*cot(Bottom angle/2))/2)
A = (2*L*t*sin(Angle_Bottom))-((((t)^2)*cot(Angle_Bottom/2))/2)

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 angle?

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

How to calculate Area of X Shape given bottom angle using this online calculator? To use this online calculator for Area of X Shape given bottom angle, enter Length (L), Thickness (t) & Bottom angle (Angle_Bottom) and hit the calculate button. Here is how the Area of X Shape given bottom angle calculation can be explained with given input values -> 1.173107 = (2*3*1*sin(0.528))-((((1)^2)*cot(0.528/2))/2).

FAQ

What is Area of X Shape given bottom angle?

The Area of X Shape given bottom angle formula is defined as the total space occupied by the X Shape in 2D space and calculated using bottom angle and is represented as A = (2*L*t*sin(Angle_Bottom))-((((t)^2)*cot(Angle_Bottom/2))/2) or Area = (2*Length*Thickness*sin(Bottom angle))-((((Thickness)^2)*cot(Bottom angle/2))/2). Length is the measurement or extent of something from end to end, Thickness is the distance through an object & The bottom angle is the bottom most angle of the given geometry.

How to calculate Area of X Shape given bottom angle?

The Area of X Shape given bottom angle formula is defined as the total space occupied by the X Shape in 2D space and calculated using bottom angle is calculated using Area = (2*Length*Thickness*sin(Bottom angle))-((((Thickness)^2)*cot(Bottom angle/2))/2). To calculate Area of X Shape given bottom angle, you need Length (L), Thickness (t) & Bottom angle (Angle_Bottom). With our tool, you need to enter the respective value for Length, Thickness & Bottom angle 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?

In this formula, Area uses Length, Thickness & Bottom angle. We can use 4 other way(s) to calculate the same, which is/are as follows -

Area = (2*Length*Thickness*sin(Top angle))-(((Crossing Length)^2)*sin(Top angle))
Area = (2*Length*Thickness*sin(Top angle))-(((Thickness^2)/2)*cot(Top angle/2))
Area = (2*Length*Thickness*sin(Left angle))-(((Crossing Length)^2)*sin(Left angle))
Area = 2*Length*Thickness*sin(Right angle)-(Thickness*sin(Right angle/2)/sin(Right angle))^2*sin(Right angle)

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