Circumradius of Isosceles Trapezoid Calculator

✖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%
✖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%

✖Circumradius of Isosceles Trapezoid is the radius of the circumcircle of the Isosceles Trapezoid or radius of the circle that contains the shape with all vertices lies on the circle.ⓘ Circumradius of Isosceles Trapezoid [r_c]

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Formula

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Circumradius of Isosceles Trapezoid

Formula

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

Example

`"7.905694m"=("5m"*sqrt(("15m"*"9m")+("5m")^2))/sqrt((4*("5m")^2)-("15m"-"9m")^2)`

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Circumradius of Isosceles Trapezoid Solution

STEP 0: Pre-Calculation Summary

Formula Used

Circumradius of Isosceles Trapezoid = (Lateral Edge of Isosceles Trapezoid*sqrt((Long Base of Isosceles Trapezoid*Short Base of Isosceles Trapezoid)+Lateral Edge of Isosceles Trapezoid^2))/sqrt((4*Lateral Edge of Isosceles Trapezoid^2)-(Long Base of Isosceles Trapezoid-Short Base of Isosceles Trapezoid)^2)
r_c = (l_e(Lateral)*sqrt((B_Long*B_Short)+l_e(Lateral)^2))/sqrt((4*l_e(Lateral)^2)-(B_Long-B_Short)^2)
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

Circumradius of Isosceles Trapezoid - (Measured in Meter) - Circumradius of Isosceles Trapezoid is the radius of the circumcircle of the Isosceles Trapezoid or radius of the circle that contains the shape with all vertices lies on the circle.
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.
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.

STEP 1: Convert Input(s) to Base Unit

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

STEP 2: Evaluate Formula

Substituting Input Values in Formula

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

Evaluating ... ...

r_c = 7.90569415042095

STEP 3: Convert Result to Output's Unit

7.90569415042095 Meter --> No Conversion Required

FINAL ANSWER

7.90569415042095 ≈ 7.905694 Meter <-- Circumradius of Isosceles Trapezoid

(Calculation completed in 00.005 seconds)

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< 3 Circumradius of Isosceles Trapezoid Calculators

Circumradius of Isosceles Trapezoid

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

Circumradius of Isosceles Trapezoid given Diagonal

Go Circumradius of Isosceles Trapezoid = Diagonal of Isosceles Trapezoid*sqrt(Diagonal of Isosceles Trapezoid^2-(Long Base of Isosceles Trapezoid*Short Base of Isosceles Trapezoid))/sqrt((4*Diagonal of Isosceles Trapezoid^2)-(Long Base of Isosceles Trapezoid+Short Base of Isosceles Trapezoid)^2)

Circumradius of Isosceles Trapezoid given Diagonal and Height

Go Circumradius of Isosceles Trapezoid = (Lateral Edge of Isosceles Trapezoid*Diagonal of Isosceles Trapezoid)/(2*Height of Isosceles Trapezoid)

< 2 Circumradius of Isosceles Trapezoid Calculators

Circumradius of Isosceles Trapezoid

Circumradius of Isosceles Trapezoid given Diagonal

Circumradius of Isosceles Trapezoid 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 Circumradius of Isosceles Trapezoid?

Circumradius of Isosceles Trapezoid calculator uses Circumradius of Isosceles Trapezoid = (Lateral Edge of Isosceles Trapezoid*sqrt((Long Base of Isosceles Trapezoid*Short Base of Isosceles Trapezoid)+Lateral Edge of Isosceles Trapezoid^2))/sqrt((4*Lateral Edge of Isosceles Trapezoid^2)-(Long Base of Isosceles Trapezoid-Short Base of Isosceles Trapezoid)^2) to calculate the Circumradius of Isosceles Trapezoid, Circumradius of Isosceles Trapezoid formula is defined as the radius of the circumcircle of the Isosceles Trapezoid or radius of the circle that contains the shape with all vertices lies on the circle. Circumradius of Isosceles Trapezoid is denoted by r_c symbol.

How to calculate Circumradius of Isosceles Trapezoid using this online calculator? To use this online calculator for Circumradius of Isosceles Trapezoid, enter Lateral Edge of Isosceles Trapezoid (l_e(Lateral)), Long Base of Isosceles Trapezoid (B_Long) & Short Base of Isosceles Trapezoid (B_Short) and hit the calculate button. Here is how the Circumradius of Isosceles Trapezoid calculation can be explained with given input values -> 7.905694 = (5*sqrt((15*9)+5^2))/sqrt((4*5^2)-(15-9)^2).

FAQ

What is Circumradius of Isosceles Trapezoid?

Circumradius of Isosceles Trapezoid formula is defined as the radius of the circumcircle of the Isosceles Trapezoid or radius of the circle that contains the shape with all vertices lies on the circle and is represented as r_c = (l_e(Lateral)*sqrt((B_Long*B_Short)+l_e(Lateral)^2))/sqrt((4*l_e(Lateral)^2)-(B_Long-B_Short)^2) or Circumradius of Isosceles Trapezoid = (Lateral Edge of Isosceles Trapezoid*sqrt((Long Base of Isosceles Trapezoid*Short Base of Isosceles Trapezoid)+Lateral Edge of Isosceles Trapezoid^2))/sqrt((4*Lateral Edge of Isosceles Trapezoid^2)-(Long Base of Isosceles Trapezoid-Short Base of Isosceles Trapezoid)^2). Lateral Edge of Isosceles Trapezoid is the length of the pair of opposite and non parallel edges of the 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.

How to calculate Circumradius of Isosceles Trapezoid?

Circumradius of Isosceles Trapezoid formula is defined as the radius of the circumcircle of the Isosceles Trapezoid or radius of the circle that contains the shape with all vertices lies on the circle is calculated using Circumradius of Isosceles Trapezoid = (Lateral Edge of Isosceles Trapezoid*sqrt((Long Base of Isosceles Trapezoid*Short Base of Isosceles Trapezoid)+Lateral Edge of Isosceles Trapezoid^2))/sqrt((4*Lateral Edge of Isosceles Trapezoid^2)-(Long Base of Isosceles Trapezoid-Short Base of Isosceles Trapezoid)^2). To calculate Circumradius of Isosceles Trapezoid, you need Lateral Edge of Isosceles Trapezoid (l_e(Lateral)), Long Base of Isosceles Trapezoid (B_Long) & Short Base of Isosceles Trapezoid (B_Short). With our tool, you need to enter the respective value for Lateral Edge of Isosceles Trapezoid, Long Base of Isosceles Trapezoid & Short Base 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 Circumradius of Isosceles Trapezoid?

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

Circumradius of Isosceles Trapezoid = Diagonal of Isosceles Trapezoid*sqrt(Diagonal of Isosceles Trapezoid^2-(Long Base of Isosceles Trapezoid*Short Base of Isosceles Trapezoid))/sqrt((4*Diagonal of Isosceles Trapezoid^2)-(Long Base of Isosceles Trapezoid+Short Base of Isosceles Trapezoid)^2)
Circumradius of Isosceles Trapezoid = (Lateral Edge of Isosceles Trapezoid*Diagonal of Isosceles Trapezoid)/(2*Height of Isosceles Trapezoid)
Circumradius of Isosceles Trapezoid = Diagonal of Isosceles Trapezoid*sqrt(Diagonal of Isosceles Trapezoid^2-(Long Base of Isosceles Trapezoid*Short Base of Isosceles Trapezoid))/sqrt((4*Diagonal of Isosceles Trapezoid^2)-(Long Base of Isosceles Trapezoid+Short Base of Isosceles Trapezoid)^2)

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