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Circumradius of Isosceles Trapezoid given Diagonal Formula

GoCircumradius of Isosceles Trapezoid Formula

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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. Check FAQs

r c = d \cdot \frac{\sqrt{d^{2} - (B Long \cdot B Short)}}{\sqrt{(4 \cdot d^{2}) - {(B Long + B Short)}^{2}}}

r_c - Circumradius of Isosceles Trapezoid?d - Diagonal of Isosceles Trapezoid?B_Long - Long Base of Isosceles Trapezoid?B_Short - Short Base of Isosceles Trapezoid?

Circumradius of Isosceles Trapezoid given Diagonal Example

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Here is how the Circumradius of Isosceles Trapezoid given Diagonal equation looks like with Values.

Here is how the Circumradius of Isosceles Trapezoid given Diagonal equation looks like with Units.

Here is how the Circumradius of Isosceles Trapezoid given Diagonal equation looks like.

7.5802 = 13 \cdot \frac{\sqrt{13^{2} - (15 \cdot 9)}}{\sqrt{(4 \cdot 13^{2}) - {(15 + 9)}^{2}}}

7.5802m = 13m \cdot \frac{\sqrt{{13m}^{2} - (15m \cdot 9m)}}{\sqrt{(4 \cdot {13m}^{2}) - {(15m + 9m)}^{2}}}

7.5802 = 13 \cdot \frac{\sqrt{13^{2} - (15 \cdot 9)}}{\sqrt{(4 \cdot 13^{2}) - {(15 + 9)}^{2}}}

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Circumradius of Isosceles Trapezoid given Diagonal Solution

Follow our step by step solution on how to calculate Circumradius of Isosceles Trapezoid given Diagonal?

FIRST Step Consider the formula

r c = d \cdot \frac{\sqrt{d^{2} - (B Long \cdot B Short)}}{\sqrt{(4 \cdot d^{2}) - {(B Long + B Short)}^{2}}}

Next Step Substitute values of Variables

∴

r c = 13m \cdot \frac{\sqrt{{13m}^{2} - (15m \cdot 9m)}}{\sqrt{(4 \cdot {13m}^{2}) - {(15m + 9m)}^{2}}}

Next Step Prepare to Evaluate

∴

r c = 13 \cdot \frac{\sqrt{13^{2} - (15 \cdot 9)}}{\sqrt{(4 \cdot 13^{2}) - {(15 + 9)}^{2}}}

Next Step Evaluate

∴

r c = 7.58023746329889m

LAST Step Rounding Answer

∴

r c = 7.5802m

Circumradius of Isosceles Trapezoid given Diagonal Formula Elements

Variables

Functions

Circumradius of Isosceles Trapezoid

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.

Symbol: r_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Circumradius of Isosceles Trapezoid

Diagonal of Isosceles Trapezoid

Diagonal of Isosceles Trapezoid is the length of the line joining any pair of opposite corners of the Isosceles Trapezoid.

Symbol: d

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Diagonal of Isosceles Trapezoid

Long Base of Isosceles Trapezoid

Long Base of Isosceles Trapezoid is the longer side among the pair of parallel sides of the Isosceles Trapezoid.

Symbol: B_Long

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Long Base of Isosceles Trapezoid

Short Base of Isosceles Trapezoid

Short Base of Isosceles Trapezoid is the shorter side among the pair of parallel sides of the Isosceles Trapezoid.

Symbol: B_Short

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Short Base of Isosceles Trapezoid

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 Circumradius of Isosceles Trapezoid

Go Circumradius of Isosceles Trapezoid

r c = \frac{l e(Lateral) \cdot \sqrt{(B Long \cdot B Short) + {l e(Lateral)}^{2}}}{\sqrt{(4 \cdot {l e(Lateral)}^{2}) - {(B Long - B Short)}^{2}}}

How to Evaluate Circumradius of Isosceles Trapezoid given Diagonal?

Circumradius of Isosceles Trapezoid given Diagonal evaluator 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 evaluate 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 evaluate Circumradius of Isosceles Trapezoid given Diagonal using this online evaluator? To use this online evaluator 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.

FAQs on Circumradius of Isosceles Trapezoid given Diagonal

What is the formula to find Circumradius of Isosceles Trapezoid given Diagonal?

The formula of Circumradius of Isosceles Trapezoid given Diagonal is expressed as 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). Here is an example- 7.580237 = 13*sqrt(13^2-(15*9))/sqrt((4*13^2)-(15+9)^2).

How to calculate Circumradius of Isosceles Trapezoid given Diagonal?

With Diagonal of Isosceles Trapezoid (d), Long Base of Isosceles Trapezoid (B_Long) & Short Base of Isosceles Trapezoid (B_Short) we can find Circumradius of Isosceles Trapezoid given Diagonal using the formula - 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). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Circumradius of Isosceles Trapezoid?

Here are the different ways to Calculate Circumradius 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)

Can the Circumradius of Isosceles Trapezoid given Diagonal be negative?

No, the Circumradius of Isosceles Trapezoid given Diagonal, measured in Length cannot be negative.

Which unit is used to measure Circumradius of Isosceles Trapezoid given Diagonal?

Circumradius of Isosceles Trapezoid given Diagonal is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Circumradius of Isosceles Trapezoid given Diagonal can be measured.

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Circumradius of Isosceles Trapezoid given Diagonal Formula

​GoCircumradius of Isosceles Trapezoid Formula

Circumradius of Isosceles Trapezoid given Diagonal Example

Circumradius of Isosceles Trapezoid given Diagonal Solution

Circumradius of Isosceles Trapezoid given Diagonal Formula Elements

Other Formulas to find Circumradius of Isosceles Trapezoid

How to Evaluate Circumradius of Isosceles Trapezoid given Diagonal?

FAQs on Circumradius of Isosceles Trapezoid given Diagonal

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GoCircumradius of Isosceles Trapezoid Formula