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Lateral Surface Area of Parallelepiped given Volume, Side A and Side C Formula

GoLateral Surface Area of Parallelepiped Formula

GoLateral Surface Area of Parallelepiped given Total Surface Area Formula

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Lateral Surface Area of Parallelepiped is the quantity of plane enclosed by all the lateral surfaces (that is, top and bottom faces are excluded) of the Parallelepiped. Check FAQs

LSA = \frac{2 \cdot V \cdot (S a \cdot \sin (∠γ) + S c \cdot \sin (∠α))}{S a \cdot S c \cdot \sqrt{1 + (2 \cdot \cos (∠α) \cdot \cos (∠β) \cdot \cos (∠γ)) - ({\cos (∠α)}^{2} + {\cos (∠β)}^{2} + {\cos (∠γ)}^{2})}}

LSA - Lateral Surface Area of Parallelepiped?V - Volume of Parallelepiped?S_a - Side A of Parallelepiped?∠γ - Angle Gamma of Parallelepiped?S_c - Side C of Parallelepiped?∠α - Angle Alpha of Parallelepiped?∠β - Angle Beta of Parallelepiped?

Lateral Surface Area of Parallelepiped given Volume, Side A and Side C Example

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Here is how the Lateral Surface Area of Parallelepiped given Volume, Side A and Side C equation looks like with Values.

Here is how the Lateral Surface Area of Parallelepiped given Volume, Side A and Side C equation looks like with Units.

Here is how the Lateral Surface Area of Parallelepiped given Volume, Side A and Side C equation looks like.

1441.9529 = \frac{2 \cdot 3630 \cdot (30 \cdot \sin (75) + 10 \cdot \sin (45))}{30 \cdot 10 \cdot \sqrt{1 + (2 \cdot \cos (45) \cdot \cos (60) \cdot \cos (75)) - ({\cos (45)}^{2} + {\cos (60)}^{2} + {\cos (75)}^{2})}}

1441.9529m² = \frac{2 \cdot 3630m³ \cdot (30m \cdot \sin (75°) + 10m \cdot \sin (45°))}{30m \cdot 10m \cdot \sqrt{1 + (2 \cdot \cos (45°) \cdot \cos (60°) \cdot \cos (75°)) - ({\cos (45°)}^{2} + {\cos (60°)}^{2} + {\cos (75°)}^{2})}}

1441.9529 = \frac{2 \cdot 3630 \cdot (30 \cdot \sin (75) + 10 \cdot \sin (45))}{30 \cdot 10 \cdot \sqrt{1 + (2 \cdot \cos (45) \cdot \cos (60) \cdot \cos (75)) - ({\cos (45)}^{2} + {\cos (60)}^{2} + {\cos (75)}^{2})}}

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Lateral Surface Area of Parallelepiped given Volume, Side A and Side C Solution

Follow our step by step solution on how to calculate Lateral Surface Area of Parallelepiped given Volume, Side A and Side C?

FIRST Step Consider the formula

LSA = \frac{2 \cdot V \cdot (S a \cdot \sin (∠γ) + S c \cdot \sin (∠α))}{S a \cdot S c \cdot \sqrt{1 + (2 \cdot \cos (∠α) \cdot \cos (∠β) \cdot \cos (∠γ)) - ({\cos (∠α)}^{2} + {\cos (∠β)}^{2} + {\cos (∠γ)}^{2})}}

Next Step Substitute values of Variables

∴

LSA = \frac{2 \cdot 3630m³ \cdot (30m \cdot \sin (75°) + 10m \cdot \sin (45°))}{30m \cdot 10m \cdot \sqrt{1 + (2 \cdot \cos (45°) \cdot \cos (60°) \cdot \cos (75°)) - ({\cos (45°)}^{2} + {\cos (60°)}^{2} + {\cos (75°)}^{2})}}

Next Step Convert Units

∴

LSA = \frac{2 \cdot 3630m³ \cdot (30m \cdot \sin (1.309rad) + 10m \cdot \sin (0.7854rad))}{30m \cdot 10m \cdot \sqrt{1 + (2 \cdot \cos (0.7854rad) \cdot \cos (1.0472rad) \cdot \cos (1.309rad)) - ({\cos (0.7854rad)}^{2} + {\cos (1.0472rad)}^{2} + {\cos (1.309rad)}^{2})}}

Next Step Prepare to Evaluate

∴

LSA = \frac{2 \cdot 3630 \cdot (30 \cdot \sin (1.309) + 10 \cdot \sin (0.7854))}{30 \cdot 10 \cdot \sqrt{1 + (2 \cdot \cos (0.7854) \cdot \cos (1.0472) \cdot \cos (1.309)) - ({\cos (0.7854)}^{2} + {\cos (1.0472)}^{2} + {\cos (1.309)}^{2})}}

Next Step Evaluate

∴

LSA = 1441.95290866899m²

LAST Step Rounding Answer

∴

LSA = 1441.9529m²

Lateral Surface Area of Parallelepiped given Volume, Side A and Side C Formula Elements

Variables

Functions

Lateral Surface Area of Parallelepiped

Lateral Surface Area of Parallelepiped is the quantity of plane enclosed by all the lateral surfaces (that is, top and bottom faces are excluded) of the Parallelepiped.

Symbol: LSA

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Lateral Surface Area of Parallelepiped

Volume of Parallelepiped

Volume of Parallelepiped is the total quantity of three-dimensional space enclosed by the surface of the Parallelepiped.

Symbol: V

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Volume of Parallelepiped

Side A of Parallelepiped

Side A of Parallelepiped is the length of any one out of the three sides from any fixed vertex of the Parallelepiped.

Symbol: S_a

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Side A of Parallelepiped

Angle Gamma of Parallelepiped

Angle Gamma of Parallelepiped is the angle formed by side A and side B at any of the two sharp tips of the Parallelepiped.

Symbol: ∠γ

Measurement: AngleUnit: °

Note: Value should be between 0 to 180.

Formulas to find Angle Gamma of Parallelepiped

Side C of Parallelepiped

Side C of Parallelepiped is the length of any one out of the three sides from any fixed vertex of the Parallelepiped.

Symbol: S_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Side C of Parallelepiped

Angle Alpha of Parallelepiped

Angle Alpha of Parallelepiped is the angle formed by side B and side C at any of the two sharp tips of the Parallelepiped.

Symbol: ∠α

Measurement: AngleUnit: °

Note: Value should be between 0 to 180.

Formulas to find Angle Alpha of Parallelepiped

Angle Beta of Parallelepiped

Angle Beta of Parallelepiped is the angle formed by side A and side C at any of the two sharp tips of the Parallelepiped.

Symbol: ∠β

Measurement: AngleUnit: °

Note: Value should be between 0 to 180.

Formulas to find Angle Beta of Parallelepiped

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.

Syntax: sin(Angle)

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: 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.

Syntax: sqrt(Number)

Other Formulas to find Lateral Surface Area of Parallelepiped

Go Lateral Surface Area of Parallelepiped

LSA = 2 \cdot ((S a \cdot S b \cdot \sin (∠γ)) + (S b \cdot S c \cdot \sin (∠α)))

Go Lateral Surface Area of Parallelepiped given Total Surface Area

LSA = TSA - 2 \cdot S a \cdot S c \cdot \sin (∠β)

How to Evaluate Lateral Surface Area of Parallelepiped given Volume, Side A and Side C?

Lateral Surface Area of Parallelepiped given Volume, Side A and Side C evaluator uses Lateral Surface Area of Parallelepiped = (2*Volume of Parallelepiped*(Side A of Parallelepiped*sin(Angle Gamma of Parallelepiped)+Side C of Parallelepiped*sin(Angle Alpha of Parallelepiped)))/(Side A of Parallelepiped*Side C of Parallelepiped*sqrt(1+(2*cos(Angle Alpha of Parallelepiped)*cos(Angle Beta of Parallelepiped)*cos(Angle Gamma of Parallelepiped))-(cos(Angle Alpha of Parallelepiped)^2+cos(Angle Beta of Parallelepiped)^2+cos(Angle Gamma of Parallelepiped)^2))) to evaluate the Lateral Surface Area of Parallelepiped, The Lateral Surface Area of Parallelepiped given Volume, Side A and Side C formula is defined as the quantity of plane enclosed by all the lateral surfaces (that is, top and bottom faces are excluded) of the Parallelepiped, calculated using volume, side A and side C of Parallelepiped. Lateral Surface Area of Parallelepiped is denoted by LSA symbol.

How to evaluate Lateral Surface Area of Parallelepiped given Volume, Side A and Side C using this online evaluator? To use this online evaluator for Lateral Surface Area of Parallelepiped given Volume, Side A and Side C, enter Volume of Parallelepiped (V), Side A of Parallelepiped (S_a), Angle Gamma of Parallelepiped (∠γ), Side C of Parallelepiped (S_c), Angle Alpha of Parallelepiped (∠α) & Angle Beta of Parallelepiped (∠β) and hit the calculate button.

FAQs on Lateral Surface Area of Parallelepiped given Volume, Side A and Side C

What is the formula to find Lateral Surface Area of Parallelepiped given Volume, Side A and Side C?

The formula of Lateral Surface Area of Parallelepiped given Volume, Side A and Side C is expressed as Lateral Surface Area of Parallelepiped = (2*Volume of Parallelepiped*(Side A of Parallelepiped*sin(Angle Gamma of Parallelepiped)+Side C of Parallelepiped*sin(Angle Alpha of Parallelepiped)))/(Side A of Parallelepiped*Side C of Parallelepiped*sqrt(1+(2*cos(Angle Alpha of Parallelepiped)*cos(Angle Beta of Parallelepiped)*cos(Angle Gamma of Parallelepiped))-(cos(Angle Alpha of Parallelepiped)^2+cos(Angle Beta of Parallelepiped)^2+cos(Angle Gamma of Parallelepiped)^2))). Here is an example- 1441.953 = (2*3630*(30*sin(1.3089969389955)+10*sin(0.785398163397301)))/(30*10*sqrt(1+(2*cos(0.785398163397301)*cos(1.0471975511964)*cos(1.3089969389955))-(cos(0.785398163397301)^2+cos(1.0471975511964)^2+cos(1.3089969389955)^2))).

How to calculate Lateral Surface Area of Parallelepiped given Volume, Side A and Side C?

With Volume of Parallelepiped (V), Side A of Parallelepiped (S_a), Angle Gamma of Parallelepiped (∠γ), Side C of Parallelepiped (S_c), Angle Alpha of Parallelepiped (∠α) & Angle Beta of Parallelepiped (∠β) we can find Lateral Surface Area of Parallelepiped given Volume, Side A and Side C using the formula - Lateral Surface Area of Parallelepiped = (2*Volume of Parallelepiped*(Side A of Parallelepiped*sin(Angle Gamma of Parallelepiped)+Side C of Parallelepiped*sin(Angle Alpha of Parallelepiped)))/(Side A of Parallelepiped*Side C of Parallelepiped*sqrt(1+(2*cos(Angle Alpha of Parallelepiped)*cos(Angle Beta of Parallelepiped)*cos(Angle Gamma of Parallelepiped))-(cos(Angle Alpha of Parallelepiped)^2+cos(Angle Beta of Parallelepiped)^2+cos(Angle Gamma of Parallelepiped)^2))). This formula also uses Sine (sin)Cosine (cos), Square Root (sqrt) function(s).

What are the other ways to Calculate Lateral Surface Area of Parallelepiped?

Here are the different ways to Calculate Lateral Surface Area of Parallelepiped-

Lateral Surface Area of Parallelepiped=2*((Side A of Parallelepiped*Side B of Parallelepiped*sin(Angle Gamma of Parallelepiped))+(Side B of Parallelepiped*Side C of Parallelepiped*sin(Angle Alpha of Parallelepiped)))
Lateral Surface Area of Parallelepiped=Total Surface Area of Parallelepiped-2*Side A of Parallelepiped*Side C of Parallelepiped*sin(Angle Beta of Parallelepiped)
Lateral Surface Area of Parallelepiped=2*((Volume of Parallelepiped*sin(Angle Gamma of Parallelepiped))/(Side C of Parallelepiped*sqrt(1+(2*cos(Angle Alpha of Parallelepiped)*cos(Angle Beta of Parallelepiped)*cos(Angle Gamma of Parallelepiped))-(cos(Angle Alpha of Parallelepiped)^2+cos(Angle Beta of Parallelepiped)^2+cos(Angle Gamma of Parallelepiped)^2)))+Side B of Parallelepiped*Side C of Parallelepiped*sin(Angle Alpha of Parallelepiped))

Can the Lateral Surface Area of Parallelepiped given Volume, Side A and Side C be negative?

No, the Lateral Surface Area of Parallelepiped given Volume, Side A and Side C, measured in Area cannot be negative.

Which unit is used to measure Lateral Surface Area of Parallelepiped given Volume, Side A and Side C?

Lateral Surface Area of Parallelepiped given Volume, Side A and Side C is usually measured using the Square Meter[m²] for Area. Square Kilometer[m²], Square Centimeter[m²], Square Millimeter[m²] are the few other units in which Lateral Surface Area of Parallelepiped given Volume, Side A and Side C can be measured.

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Lateral Surface Area of Parallelepiped given Volume, Side A and Side C Formula

​GoLateral Surface Area of Parallelepiped Formula

​GoLateral Surface Area of Parallelepiped given Total Surface Area Formula

Lateral Surface Area of Parallelepiped given Volume, Side A and Side C Example

Lateral Surface Area of Parallelepiped given Volume, Side A and Side C Solution

Lateral Surface Area of Parallelepiped given Volume, Side A and Side C Formula Elements

Other Formulas to find Lateral Surface Area of Parallelepiped

How to Evaluate Lateral Surface Area of Parallelepiped given Volume, Side A and Side C?

FAQs on Lateral Surface Area of Parallelepiped given Volume, Side A and Side C

Variable Name

GoLateral Surface Area of Parallelepiped Formula

GoLateral Surface Area of Parallelepiped given Total Surface Area Formula