Acre Calculator Using 4 Sides

Brahmagupta's Formula:

\[ \text{Area} = \sqrt{(s - a) \times (s - b) \times (s - c) \times (s - d)} \] \[ \text{where } s = \frac{a + b + c + d}{2} \text{ (semiperimeter)} \]

Side A:

Side B:

Side C:

Side D:

Calculated Area:

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1. What is Brahmagupta's Formula?

Brahmagupta's formula calculates the area of a cyclic quadrilateral (a quadrilateral that can be inscribed in a circle) given the lengths of its four sides. It's an extension of Heron's formula for triangles.

2. How Does the Calculator Work?

The calculator uses Brahmagupta's formula:

\[ \text{Area} = \sqrt{(s - a) \times (s - b) \times (s - c) \times (s - d)} \] \[ \text{where } s = \frac{a + b + c + d}{2} \text{ (semiperimeter)} \]

Where:

\( a, b, c, d \) — Lengths of the four sides
\( s \) — Semiperimeter of the quadrilateral

Explanation: The formula first calculates the semiperimeter, then uses the differences between the semiperimeter and each side to compute the area.

3. Importance of Area Calculation

Details: Accurate land area calculation is essential for property assessment, agricultural planning, construction projects, and land valuation.

4. Using the Calculator

Tips: Enter all four side lengths in feet. The calculator will compute the area in acres (1 acre = 43,560 square feet). All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: Does this formula work for all quadrilaterals?
A: It works perfectly for cyclic quadrilaterals. For other quadrilaterals, it gives the maximum possible area for the given side lengths.

Q2: What's the difference between Heron's and Brahmagupta's formulas?
A: Heron's formula is for triangles (3 sides), while Brahmagupta's extends it to cyclic quadrilaterals (4 sides).

Q3: How accurate is this calculation?
A: The calculation is mathematically exact for cyclic quadrilaterals when precise measurements are input.

Q4: Can I use different units?
A: The calculator uses feet for input and acres for output. Convert other units to feet before calculation.

Q5: What if my quadrilateral isn't cyclic?
A: The result will be the maximum possible area for those side lengths. For exact area of non-cyclic quadrilaterals, you need angle measurements.