The formula to calculate the area of a cyclic quadrilateral is:
\[ \text{Area} = \sqrt{(s - a) \times (s - b) \times (s - c) \times (s - d)} \]
Where:
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.
Example:
Step 1: Calculate the semiperimeter:
\[ s = \frac{5 + 6 + 7 + 8}{2} = 13 \text{ units} \]
Step 2: Calculate the area:
\[ \text{Area} = \sqrt{(13 - 5) \times (13 - 6) \times (13 - 7) \times (13 - 8)} = \sqrt{8 \times 7 \times 6 \times 5} = \sqrt{1680} \approx 40.99 \text{ square units} \]
