Mathematics · Geometry

Brahmagupta Cyclic-Quadrilateral Area product (s-a)(s-b) Solver

Rearrange the brahmagupta cyclic-quadrilateral area relationship and solve for product (s-a)(s-b).

Runs locally
Your numbers

Inputs and results stay in this browser. Change one value at a time to explore the relationship.

Your inputCalculatedPassed forward in chains
product (s-a)(s-b)20
Reconstructed cyclic quadrilateral area30

Calculation steps

  1. Use a=c²/b with cyclic quadrilateral area=30 and product (s-c)(s-d)=45.
  2. product (s-a)(s-b)=20.
  3. Substitution into c=√(ab) reconstructs 30.

Understand Brahmagupta Cyclic-Quadrilateral Area: solve product (s-a)(s-b)

One idea, three depths

Choose how deeply to explain Brahmagupta Cyclic-Quadrilateral Area: solve product (s-a)(s-b)

Brahmagupta Cyclic-Quadrilateral Area: solve product (s-a)(s-b): Rearrange the brahmagupta cyclic-quadrilateral area relationship and solve for product (s-a)(s-b).

Age 5Explain it to a 5-year-oldStart with a picture

Imagine using Brahmagupta Cyclic-Quadrilateral Area: solve product (s-a)(s-b) to answer this question: rearrange the brahmagupta cyclic-quadrilateral area relationship and solve for product (s-a)(s-b)? Enter cyclic quadrilateral area and product (s-c)(s-d); the calculator shows product (s-a)(s-b). For example: product (s-a)(s-b)=20 and product (s-c)(s-d)=45 produce cyclic quadrilateral area=30. The answer tells you product (s-a)(s-b).

Age 15Explain it to a 15-year-oldConnect it to the formula

Brahmagupta's formula gives cyclic-quadrilateral area as the square root of the four semiperimeter-minus-side factors. This page isolates product (s-a)(s-b) and verifies it in the original relationship. The rule is a=c²/b. Its input values are cyclic quadrilateral area, product (s-c)(s-d), and the main result is product (s-a)(s-b). For example: product (s-a)(s-b)=20 and product (s-c)(s-d)=45 produce cyclic quadrilateral area=30.

CollegeExplain it at college levelState the model precisely

This calculator evaluates the stated brahmagupta cyclic-quadrilateral area: solve product (s-a)(s-b) relation over the valid real-number domain stated below. The implemented relation is a=c²/b, evaluated from cyclic quadrilateral area, product (s-c)(s-d) to produce product (s-a)(s-b). Brahmagupta's formula gives cyclic-quadrilateral area as the square root of the four semiperimeter-minus-side factors. This page isolates product (s-a)(s-b) and verifies it in the original relationship. The quadrilateral must be cyclic and the grouped factors must be nonnegative.

Inputs and valid domain

  • cyclic quadrilateral area must be a finite real number.
  • product (s-c)(s-d) must be a finite real number.

Important boundary: The quadrilateral must be cyclic and the grouped factors must be nonnegative.

The formula

a=c²/b

How the calculator works through it

It substitutes cyclic quadrilateral area, product (s-c)(s-d) into the formula and exposes every numerical step above. The main output is product (s-a)(s-b), accompanied by Reconstructed cyclic quadrilateral area.

Read the result correctly

The product (s-a)(s-b) is the direct answer to “rearrange the brahmagupta cyclic-quadrilateral area relationship and solve for product (s-a)(s-b).” Read it with the units shown beside the inputs; a sign, angle, percentage or rate changes what the number means.

A worked check

product (s-a)(s-b)=20 and product (s-c)(s-d)=45 produce cyclic quadrilateral area=30.

Where this model stops being reliable

The quadrilateral must be cyclic and the grouped factors must be nonnegative.

Learn it by changing one value

Begin with the worked example, then change one value while keeping the others fixed. Compare the new result and calculation steps to identify which part of the formula changed.

Dictionary terms behind this calculator

Before studying the codeWhat you should know firstUse the calculator immediately, or check the foundations before reading the implementation.

These foundations help you understand why Brahmagupta Cyclic-Quadrilateral Area: solve product (s-a)(s-b) works. They never block the calculator, and “optional” means useful context rather than a hidden requirement.

Hard requirements

  • Reading formulas and substituting values

    Brahmagupta Cyclic-Quadrilateral Area: solve product (s-a)(s-b) uses a=c²/b. You need to recognise what each side represents before substituting the stated inputs or rearranging the relationship.

    Review this foundation about 4 min

Strong support

  • Ratios between measured quantities

    Ratios help you check the scale, units and proportional meaning of Brahmagupta Cyclic-Quadrilateral Area: solve product (s-a)(s-b).

    Review this foundation about 4 min

Optional enrichment

  • Angles and geometric relationships

    Angle language provides useful geometric context for extending Brahmagupta Cyclic-Quadrilateral Area: solve product (s-a)(s-b) to related shapes and constructions.

    Review this foundation about 4 min
Learn the missing foundationsI already know these — show the code

Mathematics → algorithm → program

Implement this calculation in code

These are direct reference implementations of the calculator's principal relationship and first output. They run locally and include a small known-answer check where the language supports it.

Algorithm

  1. Read cyclic quadrilateral area, product (s-c)(s-d).
  2. Evaluate the principal relationship: a=c²/b.
  3. Return product (s-a)(s-b) and check the domain conditions described above.
Python
            from math import *

def brahmagupta_cyclic_quadrilateral_area_solve_a(c, b) -> float:
    return ((c * c) / b)

assert abs(brahmagupta_cyclic_quadrilateral_area_solve_a(30, 45) - 20) < 1e-6 * max(1.0, abs(20))
          
Current calculator valuesUpdates when you change an input above.
              
            
C
            #include <assert.h>
#include <math.h>

double brahmagupta_cyclic_quadrilateral_area_solve_a(double c, double b) {
    return ((c * c) / b);
}

int main(void) {
    const double expected = 20;
    const double actual = brahmagupta_cyclic_quadrilateral_area_solve_a(30, 45);
    assert(fabs(actual - expected) < 1e-6 * fmax(1.0, fabs(expected)));
}
          
Current calculator valuesUpdates when you change an input above.
              
            
C++
            #include <cassert>
#include <cmath>
#include <numbers>

double brahmagupta_cyclic_quadrilateral_area_solve_a(double c, double b) {
    return ((c * c) / b);
}

int main() {
    constexpr double expected = 20;
    const double actual = brahmagupta_cyclic_quadrilateral_area_solve_a(30, 45);
    assert(std::fabs(actual - expected) < 1e-6 * std::fmax(1.0, std::fabs(expected)));
}
          
Current calculator valuesUpdates when you change an input above.
              
            
Linux x86-64 assembly

x86-64 NASM · System V ABI · Linux · SSE2 with libm where required

            ; double brahmagupta_cyclic_quadrilateral_area_solve_a(double c, double b)
; Linux x86-64 NASM · System V ABI · first eight doubles in xmm0–xmm7
global brahmagupta_cyclic_quadrilateral_area_solve_a
section .text

brahmagupta_cyclic_quadrilateral_area_solve_a:
    push rbp
    mov rbp, rsp
    sub rsp, 32
    movsd [rbp-8], xmm0
    movsd [rbp-16], xmm1
    movsd xmm0, [rbp-8]
    mulsd xmm0, [rbp-8]
    movsd [rbp-32], xmm0
    movsd xmm0, [rbp-32]
    divsd xmm0, [rbp-16]
    movsd [rbp-24], xmm0
    movsd xmm0, [rbp-24]
    leave
    ret
          
Current calculator valuesUpdates when you change an input above.
              
            
MATLAB
            function result = brahmagupta_cyclic_quadrilateral_area_solve_a(c, b)
    result = ((c * c) / b);
end
          
Current calculator valuesUpdates when you change an input above.
              
            
Wolfram Language
            ClearAll[mwCalculate];
mwCalculate[c_, b_] := ((c * c) / b);
          
Current calculator valuesUpdates when you change an input above.
              
            

Continue in mathematical software

The downloaded file includes your current inputs and first calculated result. It is created locally.

Floating-point answers can differ slightly by language, compiler and processor. Compare within a suitable tolerance rather than assuming every decimal representation will be identical.

Supporting sourcesAcademic referencesPrimary standards, textbooks and complete citations

Standards, reading and academic references

Use the calculator as the worked interaction, then consult the primary standards and academic textbooks listed below. MW SysArc links to the original sources; the explanation on this page is original and does not reproduce them.

Algebra and Trigonometry 2e

Read the related free OpenStax mathematics chapters
Cite this book
APA 7
Abramson, J. (2021). Algebra and trigonometry 2e. OpenStax. https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-introduction-to-prerequisites
MLA 9
Abramson, Jay. Algebra and Trigonometry 2e. OpenStax, 2021, https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-introduction-to-prerequisites.
Chicago author-date
Abramson, Jay. 2021. Algebra and Trigonometry 2e. Houston, TX: OpenStax. https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-introduction-to-prerequisites.

OpenStax entries are free to read online. Follow the licence shown on each linked source before redistributing or adapting its content.

Reuse the page responsiblyCite this pageAPA, MLA, Chicago, Harvard, BibTeX and RIS

These formats cite this calculator page itself. They are separate from the academic references above, which support the mathematical method and terminology.

APA 7

MW SysArc. (2026, July 21). Brahmagupta Cyclic-Quadrilateral Area product (s-a)(s-b) Solver. MW SysArc Tools. https://math.mwsysarc.com/geometry/brahmagupta-cyclic-quadrilateral-area-product-s-a-s-b-solver

MLA 9

MW SysArc. “Brahmagupta Cyclic-Quadrilateral Area product (s-a)(s-b) Solver.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/geometry/brahmagupta-cyclic-quadrilateral-area-product-s-a-s-b-solver. Accessed 31 Aug. 2026.

Chicago 17

MW SysArc. “Brahmagupta Cyclic-Quadrilateral Area product (s-a)(s-b) Solver.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/geometry/brahmagupta-cyclic-quadrilateral-area-product-s-a-s-b-solver.

Harvard

MW SysArc (2026) ‘Brahmagupta Cyclic-Quadrilateral Area product (s-a)(s-b) Solver’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/geometry/brahmagupta-cyclic-quadrilateral-area-product-s-a-s-b-solver (Accessed: 31 August 2026).

BibTeX and RIS records

BibTeX

@misc{mwsysarc_brahmagupta_cyclic_quadrilateral_area_solve_a_2026,
  author = {{MW SysArc}},
  title = {Brahmagupta Cyclic-Quadrilateral Area product (s-a)(s-b) Solver},
  howpublished = {MW SysArc Tools},
  year = {2026},
  url = {https://math.mwsysarc.com/geometry/brahmagupta-cyclic-quadrilateral-area-product-s-a-s-b-solver},
  note = {Published July 21, 2026; accessed August 31, 2026}
}

RIS

TY  - ELEC
AU  - MW SysArc
TI  - Brahmagupta Cyclic-Quadrilateral Area product (s-a)(s-b) Solver
T2  - MW SysArc Tools
PY  - 2026
DA  - 2026-07-21
Y2  - 2026-08-31
UR  - https://math.mwsysarc.com/geometry/brahmagupta-cyclic-quadrilateral-area-product-s-a-s-b-solver
N1  - Published July 21, 2026
ER  -

Clear answers

Frequently asked questions

What does the Brahmagupta Cyclic-Quadrilateral Area: solve product (s-a)(s-b) do?

Rearrange the brahmagupta cyclic-quadrilateral area relationship and solve for product (s-a)(s-b).

How does the Brahmagupta Cyclic-Quadrilateral Area: solve product (s-a)(s-b) work?

The calculator applies a=c²/b. Brahmagupta's formula gives cyclic-quadrilateral area as the square root of the four semiperimeter-minus-side factors. This page isolates product (s-a)(s-b) and verifies it in the original relationship.

What can I learn from the Brahmagupta Cyclic-Quadrilateral Area: solve product (s-a)(s-b)?

It connects the mathematical rule to your chosen numbers and shows each calculation step. Change one input at a time to see how the result responds.

Does MW SysArc receive or store what I enter?

No. The calculation runs locally in your browser. MW SysArc does not receive or store your calculation inputs.

How should I use the result?

Use the steps to understand the method, then verify important school or professional work using the notation and rounding rules required in your setting.

Last reviewed . Calculations tested .

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