Mathematics · Geometry
Brahmagupta Cyclic-Quadrilateral Area Calculator
Calculate cyclic quadrilateral area from product (s-a)(s-b) and product (s-c)(s-d).
Inputs and results stay in this browser. Change one value at a time to explore the relationship.
Calculation steps
- Use c=√(ab) with product (s-a)(s-b)=20 and product (s-c)(s-d)=45.
- cyclic quadrilateral area=30.
Understand Brahmagupta Cyclic-Quadrilateral Area
One idea, three depths
Choose how deeply to explain Brahmagupta Cyclic-Quadrilateral Area
Brahmagupta Cyclic-Quadrilateral Area: Calculate cyclic quadrilateral area from product (s-a)(s-b) and product (s-c)(s-d).
Age 5Explain it to a 5-year-oldStart with a picture
Imagine using Brahmagupta Cyclic-Quadrilateral Area to answer this question: calculate cyclic quadrilateral area from product (s-a)(s-b) and product (s-c)(s-d)? Enter product (s-a)(s-b) and product (s-c)(s-d); the calculator shows cyclic quadrilateral area. For example: product (s-a)(s-b)=20 and product (s-c)(s-d)=45 produce cyclic quadrilateral area=30. The answer tells you cyclic quadrilateral area.
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 evaluates the relationship directly. The rule is c=√(ab). Its input values are product (s-a)(s-b), product (s-c)(s-d), and the main result is cyclic quadrilateral area. 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 relation over the valid real-number domain stated below. The implemented relation is c=√(ab), evaluated from product (s-a)(s-b), product (s-c)(s-d) to produce cyclic quadrilateral area. Brahmagupta's formula gives cyclic-quadrilateral area as the square root of the four semiperimeter-minus-side factors. This page evaluates the relationship directly. The quadrilateral must be cyclic and the grouped factors must be nonnegative.
Inputs and valid domain
- product (s-a)(s-b) 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
c=√(ab)
How the calculator works through it
It substitutes product (s-a)(s-b), product (s-c)(s-d) into the formula and exposes every numerical step above. The main output is cyclic quadrilateral area.
Read the result correctly
The cyclic quadrilateral area is the direct answer to “calculate cyclic quadrilateral area from product (s-a)(s-b) and product (s-c)(s-d).” 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 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 uses c=√(ab). 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.
Review this foundation about 4 min
Optional enrichment
- Angles and geometric relationships
Angle language provides useful geometric context for extending Brahmagupta Cyclic-Quadrilateral Area to related shapes and constructions.
Review this foundation about 4 min
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
- Read product (s-a)(s-b), product (s-c)(s-d).
- Evaluate the principal relationship: c=√(ab).
- Return cyclic quadrilateral area and check the domain conditions described above.
Python
from math import *
def brahmagupta_cyclic_quadrilateral_area_calculator(a, b) -> float:
return sqrt((a * b))
assert abs(brahmagupta_cyclic_quadrilateral_area_calculator(20, 45) - 30) < 1e-6 * max(1.0, abs(30))
C
#include <assert.h>
#include <math.h>
double brahmagupta_cyclic_quadrilateral_area_calculator(double a, double b) {
return sqrt((a * b));
}
int main(void) {
const double expected = 30;
const double actual = brahmagupta_cyclic_quadrilateral_area_calculator(20, 45);
assert(fabs(actual - expected) < 1e-6 * fmax(1.0, fabs(expected)));
}
C++
#include <cassert>
#include <cmath>
#include <numbers>
double brahmagupta_cyclic_quadrilateral_area_calculator(double a, double b) {
return std::sqrt((a * b));
}
int main() {
constexpr double expected = 30;
const double actual = brahmagupta_cyclic_quadrilateral_area_calculator(20, 45);
assert(std::fabs(actual - expected) < 1e-6 * std::fmax(1.0, std::fabs(expected)));
}
Linux x86-64 assembly
x86-64 NASM · System V ABI · Linux · SSE2 with libm where required
; double brahmagupta_cyclic_quadrilateral_area_calculator(double a, double b)
; Linux x86-64 NASM · System V ABI · first eight doubles in xmm0–xmm7
global brahmagupta_cyclic_quadrilateral_area_calculator
section .text
brahmagupta_cyclic_quadrilateral_area_calculator:
push rbp
mov rbp, rsp
sub rsp, 32
movsd [rbp-8], xmm0
movsd [rbp-16], xmm1
movsd xmm0, [rbp-8]
mulsd xmm0, [rbp-16]
movsd [rbp-32], xmm0
sqrtsd xmm0, [rbp-32]
movsd [rbp-24], xmm0
movsd xmm0, [rbp-24]
leave
ret
MATLAB
function result = brahmagupta_cyclic_quadrilateral_area_calculator(a, b)
result = sqrt((a * b));
end
Wolfram Language
ClearAll[mwCalculate];
mwCalculate[a_, b_] := Sqrt[(a * b)];
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 chaptersCite 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 Calculator. MW SysArc Tools. https://math.mwsysarc.com/geometry/brahmagupta-cyclic-quadrilateral-area-calculator
MLA 9
MW SysArc. “Brahmagupta Cyclic-Quadrilateral Area Calculator.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/geometry/brahmagupta-cyclic-quadrilateral-area-calculator. Accessed 31 Aug. 2026.
Chicago 17
MW SysArc. “Brahmagupta Cyclic-Quadrilateral Area Calculator.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/geometry/brahmagupta-cyclic-quadrilateral-area-calculator.
Harvard
MW SysArc (2026) ‘Brahmagupta Cyclic-Quadrilateral Area Calculator’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/geometry/brahmagupta-cyclic-quadrilateral-area-calculator (Accessed: 31 August 2026).
BibTeX and RIS records
BibTeX
@misc{mwsysarc_brahmagupta_cyclic_quadrilateral_area_calculator_2026,
author = {{MW SysArc}},
title = {Brahmagupta Cyclic-Quadrilateral Area Calculator},
howpublished = {MW SysArc Tools},
year = {2026},
url = {https://math.mwsysarc.com/geometry/brahmagupta-cyclic-quadrilateral-area-calculator},
note = {Published July 21, 2026; accessed August 31, 2026}
}RIS
TY - ELEC
AU - MW SysArc
TI - Brahmagupta Cyclic-Quadrilateral Area Calculator
T2 - MW SysArc Tools
PY - 2026
DA - 2026-07-21
Y2 - 2026-08-31
UR - https://math.mwsysarc.com/geometry/brahmagupta-cyclic-quadrilateral-area-calculator
N1 - Published July 21, 2026
ER -Clear answers
Frequently asked questions
What does the Brahmagupta Cyclic-Quadrilateral Area do?
Calculate cyclic quadrilateral area from product (s-a)(s-b) and product (s-c)(s-d).
How does the Brahmagupta Cyclic-Quadrilateral Area work?
The calculator applies c=√(ab). Brahmagupta's formula gives cyclic-quadrilateral area as the square root of the four semiperimeter-minus-side factors. This page evaluates the relationship directly.
What can I learn from the Brahmagupta Cyclic-Quadrilateral Area?
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 .