The sum of the lengths of two opposite sides of the circumscribed quadrilateral is 12 cm, the length of a radius of the circle i

Question

romanna [79]

3 years ago

14

The sum of the lengths of two opposite sides of the circumscribed quadrilateral is 12 cm, the length of a radius of the circle i

s 5 cm. Find the area of the quadrilateral

Mathematics

1 answer:

nasty-shy [4] · Answer 1 · 2022-03-27T04:32:10+03:00

Answer:

60cm^2

Step-by-step 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) (5cm) = 60 cm²

_____

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