Brahmagupta’s Formula Calculator

Brahmagupta, a renowned Indian mathematician, provided this formula for calculating the area of four-sided shapes where all corners lie on a circle. Enter the side lengths into the calculator, and it will apply Brahmagupta’s formula to give you an accurate area result.

The Brahmagupta’s Formula Calculator allows you to quickly calculate the area of a cyclic quadrilateral based on its side lengths.

Formula:

Brahmagupta’s Formula provides a simple yet powerful method for calculating the area of a quadrilateral. Here’s the formula:

$\text{Area=(S−a)(S−b)(S−C)(S−d)}$​

Variables

How to Calculate ?

1. Add the lengths of all four sides together:

   $$s = \frac{a + b + c + d}{2}$$

   This gives you the semi-perimeter (s). It’s the total of the four sides divided by 2.

2. Subtract each side length from the semi-perimeter: For each side, you will calculate $s – a$, $s – b$, $s – c$, and $s – d$.

3. Multiply all these results together:

   $$(s – a) \times (s – b) \times (s – c) \times (s – d)$$

4. Take the square root of the result from step 3 to find the area:

   $$\text{Area} = \sqrt{(s – a) \times (s – b) \times (s – c) \times (s – d)$$

Example:

If the sides are 8, 6, 5, and 7:

1. Add the sides:
   $s = \frac{8 + 6 + 5 + 7}{2} = 13$

2. Subtract each side from $s$:
   $s – a = 13 – 8 = 5$
   $s – b = 13 – 6 = 7$
   $s – c = 13 – 5 = 8$
   $s – d = 13 – 7 = 6$

3. Multiply these results:
   $5 \times 7 \times 8 \times 6 = 1680$

4. Take the square root:
   $\sqrt{1680} = 40.99$

Answer: The area is 40.99 square units.

What is Brahmagupta’s Formula Calculator ?

Brahmagupta, an ancient Indian mathematician, provided a formula to determine the area of a cyclic quadrilateral if the lengths of its sides are known. This calculator is vitally useful to calculate the area of a cyclic quadrilateral, which is a four-sided shape where all vertices lie on a circle.

Particularly it is useful in geometry, allowing for accurate area calculations without needing to know the angles of the quadrilateral.

Brahmagupta’s contributions to mathematics go beyond this formula. He made significant advancements in algebra and trigonometry, including the development of rules for zero and negative numbers.

Final Words:

The calculator makes the process of  calculating the area of cyclic quadrilaterals, all easy. It is must have tool for students, teachers, and engineers.