Enter the lengths of all four sides of a cyclic quadrilateral into the calculator to determine the area using Brahmagupta’s formula.

Brahmagupta’s Formula Calculator

Enter the lengths of the four sides to calculate the area

Brahmagupta's Formula

The following formula is used to calculate the area of a cyclic quadrilateral:

Area = √((s - a) * (s - b) * (s - c) * (s - d))

where:

  • s is the semiperimeter of the quadrilateral (s = (a + b + c + d) / 2)
  • a, b, c, d are the lengths of the sides of the quadrilateral

To calculate the area of a cyclic quadrilateral, first determine the semiperimeter (s), then use Brahmagupta's formula by plugging in the lengths of the sides.

What is a Cyclic Quadrilateral?

A cyclic quadrilateral is a four-sided figure where all four vertices lie on the circumference of a circle. This type of quadrilateral has special properties, such as opposite angles that add up to 180 degrees. The area of a cyclic quadrilateral can be calculated using Brahmagupta's formula if the lengths of all sides are known.

How to Calculate the Area of a Cyclic Quadrilateral?

The following steps outline how to calculate the area of a cyclic quadrilateral:

  1. Measure the lengths of all four sides of the cyclic quadrilateral (a, b, c, d).
  2. Calculate the semiperimeter (s) using the formula s = (a + b + c + d) / 2.
  3. Use Brahmagupta's formula to calculate the area: Area = √((s - a) * (s - b) * (s - c) * (s - d)).
  4. Enter the side lengths into the calculator above to verify your result.

Example Problem:

Use the following side lengths as an example problem to test your knowledge:

Side A (a) = 5 units

Side B (b) = 6 units

Side C (c) = 7 units

Side D (d) = 8 units