Question

Use Brahmagupta's Formula

✓(s−a)(s−b)(s−c)(s−d) to find the area of a cyclic quadrilateral whose sides measure 6 in., 7 in., 2 in., and 9 in. Here s= 21 (a+b+c+d) denotes the quadrilateral's semiperimeter.

Answer 1

To find the area of a cyclic quadrilateral, use Brahmagupta's formula by substituting the lengths of the sides and the semiperimeter into the formula.

Step-by-step explanation:

To find the area of a cyclic quadrilateral, we can use Brahmagupta's formula: √((s-a)(s-b)(s-c)(s-d)), where s is the semiperimeter and a, b, c, d are the lengths of the sides of the quadrilateral. In this case, we have s = 21 (6+7+2+9) = 24. The formula becomes √((24-6)(24-7)(24-2)(24-9)).

Calculating this expression, we get √(18*17*22*15) = √{{65340}}. Simplifying further, we have √{{4,356,360}}. Therefore, the area of the cyclic quadrilateral is approximately 4,356,360 square units.