Calculate the area of a cyclic quadrilateral with Brahmagupta’s formula from four side lengths in meters, centimeters, inches, or feet.
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Brahmagupta’s Formula Formula
Brahmagupta’s formula finds the area of a cyclic quadrilateral from its four side lengths. A cyclic quadrilateral is a four-sided shape whose vertices all lie on one circle.
s = (a + b + c + d)/2
A = sqrt((s - a)(s - b)(s - c)(s - d))
For unit handling, the calculator first converts all side lengths to meters, calculates the area in square meters, then converts the result to your selected area unit.
length_m = length * length_conversion_factor
A_selected = A_m2 * area_conversion_factor
- a, b, c, d = the four side lengths of the quadrilateral
- s = semiperimeter, or half the total perimeter
- A = area of the cyclic quadrilateral
- length_m = a side length converted to meters
- A_m2 = area in square meters
- A_selected = area converted to the selected output unit
The calculate function reads the four side lengths, converts them to meters if needed, finds the semiperimeter, applies Brahmagupta’s formula, and displays the area in the chosen square unit. The reset function clears all side inputs and returns the units to their default settings.
Unit Conversions Used for Side Lengths and Area
The side lengths can be entered in different units. Internally, each side is converted to meters before the area is calculated.
| Input unit | Conversion to meters |
|---|---|
| Meters | 1 m = 1 m |
| Centimeters | 1 cm = 0.01 m |
| Inches | 1 in = 0.0254 m |
| Feet | 1 ft = 0.3048 m |
| Output unit | Conversion from square meters |
|---|---|
| Square meters | 1 m² = 1 m² |
| Square centimeters | 1 m² = 10,000 cm² |
| Square inches | 1 m² ≈ 1550.0031 in² |
| Square feet | 1 m² ≈ 10.7639 ft² |
Example Calculations
Example 1: Four sides in meters
Find the area of a cyclic quadrilateral with side lengths 5 m, 6 m, 7 m, and 8 m.
s = (5 + 6 + 7 + 8)/2 = 13
A = sqrt((13 - 5)(13 - 6)(13 - 7)(13 - 8))
A = sqrt(8*7*6*5) = sqrt(1680) = 40.9878 m^2
The calculated area is approximately 40.9878 m².
Example 2: Rectangle side lengths in feet
A rectangle is cyclic, so Brahmagupta’s formula works for a rectangle. Use side lengths 10 ft, 6 ft, 10 ft, and 6 ft.
s = (10 + 6 + 10 + 6)/2 = 16
A = sqrt((16 - 10)(16 - 6)(16 - 10)(16 - 6))
A = sqrt(6*10*6*10) = sqrt(3600) = 60 ft^2
The calculated area is 60 ft².
FAQ
When can you use Brahmagupta’s formula?
You can use it when the quadrilateral is cyclic, meaning all four vertices lie on a single circle. Rectangles, squares, and isosceles trapezoids are common examples of cyclic quadrilaterals. If the quadrilateral is not cyclic, the same four side lengths may not give the actual area of that shape.
Why does the calculator ask for only the side lengths?
Brahmagupta’s formula is based only on the four side lengths, but that works specifically for cyclic quadrilaterals. You do not need angles or diagonals if the shape is cyclic.
What does it mean if the side lengths are invalid?
The side lengths must be able to form a quadrilateral. In practical terms, the longest side must be shorter than the sum of the other three sides. If this condition is not met, the formula produces an invalid result because no closed quadrilateral can be formed from those lengths.
