Long Diagonal of Trapezoid given all Sides Calculator

✖Short Leg of Trapezoid is the shorter side among the pair of non parallel and opposite sides of the Trapezoid.ⓘ Short Leg of Trapezoid [L_Short]			+10% -10%
✖Short Base of Trapezoid is the shorter side among the pair of parallel sides of the Trapezoid.ⓘ Short Base of Trapezoid [B_Short]			+10% -10%
✖Long Base of Trapezoid is the longer side among the pair of parallel sides of the Trapezoid.ⓘ Long Base of Trapezoid [B_Long]			+10% -10%
✖Long Leg of Trapezoid is the longer side among the pair of non parallel and opposite sides of the Trapezoid.ⓘ Long Leg of Trapezoid [L_Long]			+10% -10%

✖Long Diagonal of Trapezoid is the length of the line joining the corners of smaller acute angle and smaller obtuse angle of the Trapezoid.ⓘ Long Diagonal of Trapezoid given all Sides [d_Long]

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Long Diagonal of Trapezoid given all Sides Solution

STEP 0: Pre-Calculation Summary

Formula Used

Long Diagonal of Trapezoid = sqrt(Short Leg of Trapezoid^2+(Short Base of Trapezoid*Long Base of Trapezoid)-(Long Base of Trapezoid*(Short Leg of Trapezoid^2-Long Leg of Trapezoid^2)/(Long Base of Trapezoid-Short Base of Trapezoid)))
d_Long = sqrt(L_Short^2+(B_Short*B_Long)-(B_Long*(L_Short^2-L_Long^2)/(B_Long-B_Short)))
This formula uses 1 Functions, 5 Variables

Functions Used

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

Long Diagonal of Trapezoid - (Measured in Meter) - Long Diagonal of Trapezoid is the length of the line joining the corners of smaller acute angle and smaller obtuse angle of the Trapezoid.
Short Leg of Trapezoid - (Measured in Meter) - Short Leg of Trapezoid is the shorter side among the pair of non parallel and opposite sides of the Trapezoid.
Short Base of Trapezoid - (Measured in Meter) - Short Base of Trapezoid is the shorter side among the pair of parallel sides of the Trapezoid.
Long Base of Trapezoid - (Measured in Meter) - Long Base of Trapezoid is the longer side among the pair of parallel sides of the Trapezoid.
Long Leg of Trapezoid - (Measured in Meter) - Long Leg of Trapezoid is the longer side among the pair of non parallel and opposite sides of the Trapezoid.

STEP 1: Convert Input(s) to Base Unit

Short Leg of Trapezoid: 9 Meter --> 9 Meter No Conversion Required
Short Base of Trapezoid: 5 Meter --> 5 Meter No Conversion Required
Long Base of Trapezoid: 15 Meter --> 15 Meter No Conversion Required
Long Leg of Trapezoid: 11 Meter --> 11 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d_Long = sqrt(L_Short^2+(B_Short*B_Long)-(B_Long*(L_Short^2-L_Long^2)/(B_Long-B_Short))) --> sqrt(9^2+(5*15)-(15*(9^2-11^2)/(15-5)))

Evaluating ... ...

d_Long = 14.6969384566991

STEP 3: Convert Result to Output's Unit

14.6969384566991 Meter --> No Conversion Required

FINAL ANSWER

14.6969384566991 ≈ 14.69694 Meter <-- Long Diagonal of Trapezoid

(Calculation completed in 00.020 seconds)

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< Long Diagonal of Trapezoid Calculators

Long Diagonal of Trapezoid given all Sides

LaTeX Go Long Diagonal of Trapezoid = sqrt(Short Leg of Trapezoid^2+(Short Base of Trapezoid*Long Base of Trapezoid)-(Long Base of Trapezoid*(Short Leg of Trapezoid^2-Long Leg of Trapezoid^2)/(Long Base of Trapezoid-Short Base of Trapezoid)))

Long Diagonal of Trapezoid given Long Leg

LaTeX Go Long Diagonal of Trapezoid = sqrt(Short Base of Trapezoid^2+Long Leg of Trapezoid^2-(2*Short Base of Trapezoid*Long Leg of Trapezoid*cos(Larger Obtuse Angle of Trapezoid)))

Long Diagonal of Trapezoid

LaTeX Go Long Diagonal of Trapezoid = sqrt(Long Base of Trapezoid^2+Short Leg of Trapezoid^2-(2*Long Base of Trapezoid*Short Leg of Trapezoid*cos(Larger Acute Angle of Trapezoid)))

Long Diagonal of Trapezoid given Height and Larger Acute Angle

LaTeX Go Long Diagonal of Trapezoid = sqrt(Height of Trapezoid^2+(Long Base of Trapezoid-(Height of Trapezoid*cot(Larger Acute Angle of Trapezoid)))^2)

< Diagonal of Trapezoid Calculators

Long Diagonal of Trapezoid given all Sides

Short Diagonal of Trapezoid

LaTeX Go Short Diagonal of Trapezoid = sqrt(Long Base of Trapezoid^2+Long Leg of Trapezoid^2-(2*Long Base of Trapezoid*Long Leg of Trapezoid*cos(Smaller Acute Angle of Trapezoid)))

Long Diagonal of Trapezoid

LaTeX Go Long Diagonal of Trapezoid = sqrt(Long Base of Trapezoid^2+Short Leg of Trapezoid^2-(2*Long Base of Trapezoid*Short Leg of Trapezoid*cos(Larger Acute Angle of Trapezoid)))

Long Diagonal of Trapezoid given Short Diagonal

LaTeX Go Long Diagonal of Trapezoid = (Height of Trapezoid*(Long Base of Trapezoid+Short Base of Trapezoid))/(Short Diagonal of Trapezoid*sin(Leg Angle between Diagonals of Trapezoid))

Long Diagonal of Trapezoid given all Sides Formula

LaTeX Go

What is a Trapezoid?

Trapezoid is a quadrilateral with one pair of opposite and parallel sides. The pair of parallel sides is called the bases of the Trapezoid and the pair of non parallel edges is called the legs of the Trapezoid. Out of the four angles, in general a Trapezoid has 2 acute angles and 2 obtuse angles which are pairwise supplementary angles.

How to Calculate Long Diagonal of Trapezoid given all Sides?

Long Diagonal of Trapezoid given all Sides calculator uses Long Diagonal of Trapezoid = sqrt(Short Leg of Trapezoid^2+(Short Base of Trapezoid*Long Base of Trapezoid)-(Long Base of Trapezoid*(Short Leg of Trapezoid^2-Long Leg of Trapezoid^2)/(Long Base of Trapezoid-Short Base of Trapezoid))) to calculate the Long Diagonal of Trapezoid, Long Diagonal of Trapezoid given all Sides formula is defined as the length of the line joining the corners of smaller acute angle and smaller obtuse angle of the Trapezoid, and calculated using all sides of the Trapezoid. Long Diagonal of Trapezoid is denoted by d_Long symbol.

How to calculate Long Diagonal of Trapezoid given all Sides using this online calculator? To use this online calculator for Long Diagonal of Trapezoid given all Sides, enter Short Leg of Trapezoid (L_Short), Short Base of Trapezoid (B_Short), Long Base of Trapezoid (B_Long) & Long Leg of Trapezoid (L_Long) and hit the calculate button. Here is how the Long Diagonal of Trapezoid given all Sides calculation can be explained with given input values -> 14.69694 = sqrt(9^2+(5*15)-(15*(9^2-11^2)/(15-5))).

FAQ

What is Long Diagonal of Trapezoid given all Sides?

Long Diagonal of Trapezoid given all Sides formula is defined as the length of the line joining the corners of smaller acute angle and smaller obtuse angle of the Trapezoid, and calculated using all sides of the Trapezoid and is represented as d_Long = sqrt(L_Short^2+(B_Short*B_Long)-(B_Long*(L_Short^2-L_Long^2)/(B_Long-B_Short))) or Long Diagonal of Trapezoid = sqrt(Short Leg of Trapezoid^2+(Short Base of Trapezoid*Long Base of Trapezoid)-(Long Base of Trapezoid*(Short Leg of Trapezoid^2-Long Leg of Trapezoid^2)/(Long Base of Trapezoid-Short Base of Trapezoid))). Short Leg of Trapezoid is the shorter side among the pair of non parallel and opposite sides of the Trapezoid, Short Base of Trapezoid is the shorter side among the pair of parallel sides of the Trapezoid, Long Base of Trapezoid is the longer side among the pair of parallel sides of the Trapezoid & Long Leg of Trapezoid is the longer side among the pair of non parallel and opposite sides of the Trapezoid.

How to calculate Long Diagonal of Trapezoid given all Sides?

Long Diagonal of Trapezoid given all Sides formula is defined as the length of the line joining the corners of smaller acute angle and smaller obtuse angle of the Trapezoid, and calculated using all sides of the Trapezoid is calculated using Long Diagonal of Trapezoid = sqrt(Short Leg of Trapezoid^2+(Short Base of Trapezoid*Long Base of Trapezoid)-(Long Base of Trapezoid*(Short Leg of Trapezoid^2-Long Leg of Trapezoid^2)/(Long Base of Trapezoid-Short Base of Trapezoid))). To calculate Long Diagonal of Trapezoid given all Sides, you need Short Leg of Trapezoid (L_Short), Short Base of Trapezoid (B_Short), Long Base of Trapezoid (B_Long) & Long Leg of Trapezoid (L_Long). With our tool, you need to enter the respective value for Short Leg of Trapezoid, Short Base of Trapezoid, Long Base of Trapezoid & Long Leg of Trapezoid 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 Long Diagonal of Trapezoid?

In this formula, Long Diagonal of Trapezoid uses Short Leg of Trapezoid, Short Base of Trapezoid, Long Base of Trapezoid & Long Leg of Trapezoid. We can use 3 other way(s) to calculate the same, which is/are as follows -

Long Diagonal of Trapezoid = sqrt(Long Base of Trapezoid^2+Short Leg of Trapezoid^2-(2*Long Base of Trapezoid*Short Leg of Trapezoid*cos(Larger Acute Angle of Trapezoid)))
Long Diagonal of Trapezoid = sqrt(Short Base of Trapezoid^2+Long Leg of Trapezoid^2-(2*Short Base of Trapezoid*Long Leg of Trapezoid*cos(Larger Obtuse Angle of Trapezoid)))
Long Diagonal of Trapezoid = sqrt(Height of Trapezoid^2+(Long Base of Trapezoid-(Height of Trapezoid*cot(Larger Acute Angle of Trapezoid)))^2)

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