Question

The sum of the lengths of two opposite sides of the circumscribed quadrilateral is 12 cm, the length of a radius of the circle is 2 cm. Find the area of the quadrilateral.

Answer 1

24 cm²

Explanation:

We assume that is a circumscribing quadrilateral, rather than one that is circumscribed. It is also called a "tangential quadrilateral" and its area is ...

K = sr

where s is the semi-perimeter, the sum of opposite sides, and r is the radius of the incircle.

K = (12 cm)(2 cm) = 24 cm²

_____

A quadrilateral can only be tangential if pairs of opposite sides add to the same length. Hence the given sum is the semiperimeter.