Circumradius of Isosceles Trapezoid given Diagonal Calculator

✖Diagonal of Isosceles Trapezoid is the length of the line joining any pair of opposite corners of the Isosceles Trapezoid.ⓘ Diagonal of Isosceles Trapezoid [d]			+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 given Diagonal [r_c]

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Circumradius of Isosceles Trapezoid given Diagonal Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
r_c = d*sqrt(d^2-(B_Long*B_Short))/sqrt((4*d^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.
Diagonal of Isosceles Trapezoid - (Measured in Meter) - Diagonal of Isosceles Trapezoid is the length of the line joining any pair of opposite corners 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

Diagonal of Isosceles Trapezoid: 13 Meter --> 13 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 = d*sqrt(d^2-(B_Long*B_Short))/sqrt((4*d^2)-(B_Long+B_Short)^2) --> 13*sqrt(13^2-(15*9))/sqrt((4*13^2)-(15+9)^2)

Evaluating ... ...

r_c = 7.58023746329889

STEP 3: Convert Result to Output's Unit

7.58023746329889 Meter --> No Conversion Required

FINAL ANSWER

7.58023746329889 ≈ 7.580237 Meter <-- Circumradius of Isosceles Trapezoid

(Calculation completed in 00.020 seconds)

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< Circumradius of Isosceles Trapezoid Calculators

Circumradius of Isosceles Trapezoid

LaTeX 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

LaTeX 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

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

< Circumradius of Isosceles Trapezoid Calculators

Circumradius of Isosceles Trapezoid

Circumradius of Isosceles Trapezoid given Diagonal

Circumradius of Isosceles Trapezoid given Diagonal Formula

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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 given Diagonal?

Circumradius of Isosceles Trapezoid given Diagonal calculator uses 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) to calculate the Circumradius of Isosceles Trapezoid, Circumradius of Isosceles Trapezoid given Diagonal 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 calculated using diagonal of the Isosceles Trapezoid. Circumradius of Isosceles Trapezoid is denoted by r_c symbol.

How to calculate Circumradius of Isosceles Trapezoid given Diagonal using this online calculator? To use this online calculator for Circumradius of Isosceles Trapezoid given Diagonal, enter Diagonal of Isosceles Trapezoid (d), 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 given Diagonal calculation can be explained with given input values -> 7.580237 = 13*sqrt(13^2-(15*9))/sqrt((4*13^2)-(15+9)^2).

FAQ

What is Circumradius of Isosceles Trapezoid given Diagonal?

Circumradius of Isosceles Trapezoid given Diagonal 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 calculated using diagonal of the Isosceles Trapezoid and is represented as r_c = d*sqrt(d^2-(B_Long*B_Short))/sqrt((4*d^2)-(B_Long+B_Short)^2) or 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). Diagonal of Isosceles Trapezoid is the length of the line joining any pair of opposite corners 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 given Diagonal?

Circumradius of Isosceles Trapezoid given Diagonal 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 calculated using diagonal of the Isosceles Trapezoid is calculated using 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). To calculate Circumradius of Isosceles Trapezoid given Diagonal, you need Diagonal of Isosceles Trapezoid (d), 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 Diagonal 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 Diagonal 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 = (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 = (Lateral Edge of Isosceles Trapezoid*Diagonal of Isosceles Trapezoid)/(2*Height of Isosceles Trapezoid)
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)

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