Area of Isosceles Trapezoid given Lateral Edge Calculator

✖Long Base of Isosceles Trapezoid is the longer side among the pair of parallel sides of the Isosceles Trapezoid.ⓘ Long Base of Isosceles Trapezoid [B_Long]			+10% -10%
✖Short Base of Isosceles Trapezoid is the shorter side among the pair of parallel sides of the Isosceles Trapezoid.ⓘ Short Base of Isosceles Trapezoid [B_Short]			+10% -10%
✖Lateral Edge of Isosceles Trapezoid is the length of the pair of opposite and non parallel edges of the Isosceles Trapezoid.ⓘ Lateral Edge of Isosceles Trapezoid [l_e(Lateral)]			+10% -10%

✖Area of Isosceles Trapezoid is the total quantity of plane enclosed by the boundary of the Isosceles Trapezoid.ⓘ Area of Isosceles Trapezoid given Lateral Edge [A]

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Formula

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Area of Isosceles Trapezoid given Lateral Edge

Formula

`"A" = 1/4*sqrt(("B"_{"Long"}+"B"_{"Short"})^2*("B"_{"Long"}-"B"_{"Short"}+(2*"l"_{"e(Lateral)"}))*("B"_{"Short"}-"B"_{"Long"}+(2*"l"_{"e(Lateral)"})))`

Example

`"48m²"=1/4*sqrt(("15m"+"9m")^2*("15m"-"9m"+(2*"5m"))*("9m"-"15m"+(2*"5m")))`

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Area of Isosceles Trapezoid given Lateral Edge Solution

STEP 0: Pre-Calculation Summary

Formula Used

Area of Isosceles Trapezoid = 1/4*sqrt((Long Base of Isosceles Trapezoid+Short Base of Isosceles Trapezoid)^2*(Long Base of Isosceles Trapezoid-Short Base of Isosceles Trapezoid+(2*Lateral Edge of Isosceles Trapezoid))*(Short Base of Isosceles Trapezoid-Long Base of Isosceles Trapezoid+(2*Lateral Edge of Isosceles Trapezoid)))
A = 1/4*sqrt((B_Long+B_Short)^2*(B_Long-B_Short+(2*l_e(Lateral)))*(B_Short-B_Long+(2*l_e(Lateral))))
This formula uses 1 Functions, 4 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

Area of Isosceles Trapezoid - (Measured in Square Meter) - Area of Isosceles Trapezoid is the total quantity of plane enclosed by the boundary of the Isosceles Trapezoid.
Long Base of Isosceles Trapezoid - (Measured in Meter) - Long Base of Isosceles Trapezoid is the longer side among the pair of parallel sides of the Isosceles Trapezoid.
Short Base of Isosceles Trapezoid - (Measured in Meter) - Short Base of Isosceles Trapezoid is the shorter side among the pair of parallel sides of the Isosceles Trapezoid.
Lateral Edge of Isosceles Trapezoid - (Measured in Meter) - Lateral Edge of Isosceles Trapezoid is the length of the pair of opposite and non parallel edges of the Isosceles Trapezoid.

STEP 1: Convert Input(s) to Base Unit

Long Base of Isosceles Trapezoid: 15 Meter --> 15 Meter No Conversion Required
Short Base of Isosceles Trapezoid: 9 Meter --> 9 Meter No Conversion Required
Lateral Edge of Isosceles Trapezoid: 5 Meter --> 5 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A = 1/4*sqrt((B_Long+B_Short)^2*(B_Long-B_Short+(2*l_e(Lateral)))*(B_Short-B_Long+(2*l_e(Lateral)))) --> 1/4*sqrt((15+9)^2*(15-9+(2*5))*(9-15+(2*5)))

Evaluating ... ...

A = 48

STEP 3: Convert Result to Output's Unit

48 Square Meter --> No Conversion Required

FINAL ANSWER

48 Square Meter <-- Area of Isosceles Trapezoid

(Calculation completed in 00.004 seconds)

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< 3 Area of Isosceles Trapezoid Calculators

Area of Isosceles Trapezoid given Lateral Edge

Go Area of Isosceles Trapezoid = 1/4*sqrt((Long Base of Isosceles Trapezoid+Short Base of Isosceles Trapezoid)^2*(Long Base of Isosceles Trapezoid-Short Base of Isosceles Trapezoid+(2*Lateral Edge of Isosceles Trapezoid))*(Short Base of Isosceles Trapezoid-Long Base of Isosceles Trapezoid+(2*Lateral Edge of Isosceles Trapezoid)))

Area of Isosceles Trapezoid

Go Area of Isosceles Trapezoid = ((Long Base of Isosceles Trapezoid+Short Base of Isosceles Trapezoid)/2)*Height of Isosceles Trapezoid

Area of Isosceles Trapezoid given Central Median and Height

Go Area of Isosceles Trapezoid = Central Median of Isosceles Trapezoid*Height of Isosceles Trapezoid

Area of Isosceles Trapezoid given Lateral Edge Formula

What is an Isosceles Trapezoid?

A Trapezoid is a quadrilateral with one pair of parallel edges. An Isosceles Trapezoid means a trapezoid with the pair of non parallel edges are equal. The parallel pair of edges are called bases and the pair of non parallel equal edges are called lateral edges. The angles on the long base are equal acute angles and the angles on the short base are equal obtuse angles. Also, the pair of opposite angles are supplementary to each other. And hence an Isosceles Trapezoid is cyclic.

How to Calculate Area of Isosceles Trapezoid given Lateral Edge?

Area of Isosceles Trapezoid given Lateral Edge calculator uses Area of Isosceles Trapezoid = 1/4*sqrt((Long Base of Isosceles Trapezoid+Short Base of Isosceles Trapezoid)^2*(Long Base of Isosceles Trapezoid-Short Base of Isosceles Trapezoid+(2*Lateral Edge of Isosceles Trapezoid))*(Short Base of Isosceles Trapezoid-Long Base of Isosceles Trapezoid+(2*Lateral Edge of Isosceles Trapezoid))) to calculate the Area of Isosceles Trapezoid, Area of Isosceles Trapezoid given Lateral Edge formula is defined as the total quantity of plane enclosed by the boundary of the Isosceles Trapezoid, and calculated using the lateral edge of the Isosceles Trapezoid. Area of Isosceles Trapezoid is denoted by A symbol.

How to calculate Area of Isosceles Trapezoid given Lateral Edge using this online calculator? To use this online calculator for Area of Isosceles Trapezoid given Lateral Edge, enter Long Base of Isosceles Trapezoid (B_Long), Short Base of Isosceles Trapezoid (B_Short) & Lateral Edge of Isosceles Trapezoid (l_e(Lateral)) and hit the calculate button. Here is how the Area of Isosceles Trapezoid given Lateral Edge calculation can be explained with given input values -> 48 = 1/4*sqrt((15+9)^2*(15-9+(2*5))*(9-15+(2*5))).

FAQ

What is Area of Isosceles Trapezoid given Lateral Edge?

Area of Isosceles Trapezoid given Lateral Edge formula is defined as the total quantity of plane enclosed by the boundary of the Isosceles Trapezoid, and calculated using the lateral edge of the Isosceles Trapezoid and is represented as A = 1/4*sqrt((B_Long+B_Short)^2*(B_Long-B_Short+(2*l_e(Lateral)))*(B_Short-B_Long+(2*l_e(Lateral)))) or Area of Isosceles Trapezoid = 1/4*sqrt((Long Base of Isosceles Trapezoid+Short Base of Isosceles Trapezoid)^2*(Long Base of Isosceles Trapezoid-Short Base of Isosceles Trapezoid+(2*Lateral Edge of Isosceles Trapezoid))*(Short Base of Isosceles Trapezoid-Long Base of Isosceles Trapezoid+(2*Lateral Edge of Isosceles Trapezoid))). Long Base of Isosceles Trapezoid is the longer side among the pair of parallel sides of the Isosceles Trapezoid, Short Base of Isosceles Trapezoid is the shorter side among the pair of parallel sides of the Isosceles Trapezoid & Lateral Edge of Isosceles Trapezoid is the length of the pair of opposite and non parallel edges of the Isosceles Trapezoid.

How to calculate Area of Isosceles Trapezoid given Lateral Edge?

Area of Isosceles Trapezoid given Lateral Edge formula is defined as the total quantity of plane enclosed by the boundary of the Isosceles Trapezoid, and calculated using the lateral edge of the Isosceles Trapezoid is calculated using Area of Isosceles Trapezoid = 1/4*sqrt((Long Base of Isosceles Trapezoid+Short Base of Isosceles Trapezoid)^2*(Long Base of Isosceles Trapezoid-Short Base of Isosceles Trapezoid+(2*Lateral Edge of Isosceles Trapezoid))*(Short Base of Isosceles Trapezoid-Long Base of Isosceles Trapezoid+(2*Lateral Edge of Isosceles Trapezoid))). To calculate Area of Isosceles Trapezoid given Lateral Edge, you need Long Base of Isosceles Trapezoid (B_Long), Short Base of Isosceles Trapezoid (B_Short) & Lateral Edge of Isosceles Trapezoid (l_e(Lateral)). With our tool, you need to enter the respective value for Long Base of Isosceles Trapezoid, Short Base of Isosceles Trapezoid & Lateral Edge of Isosceles 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 Area of Isosceles Trapezoid?

In this formula, Area of Isosceles Trapezoid uses Long Base of Isosceles Trapezoid, Short Base of Isosceles Trapezoid & Lateral Edge of Isosceles Trapezoid. We can use 2 other way(s) to calculate the same, which is/are as follows -

Area of Isosceles Trapezoid = Central Median of Isosceles Trapezoid*Height of Isosceles Trapezoid
Area of Isosceles Trapezoid = ((Long Base of Isosceles Trapezoid+Short Base of Isosceles Trapezoid)/2)*Height of Isosceles Trapezoid

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