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
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:
- Measure the lengths of all four sides of the cyclic quadrilateral (a, b, c, d).
- Calculate the semiperimeter (s) using the formula s = (a + b + c + d) / 2.
- Use Brahmagupta’s formula to calculate the area: Area = √((s – a) * (s – b) * (s – c) * (s – d)).
- 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
