The Product of the Inradius and Semiperimeter of a Triangle

show r

AB

≈

6.62

BC

≈

6.22

AC

≈

7.80

r

≈

1.92

s

≈

10.32

area(ABC)

≈

19.85

r

×

s

≈

19.85

Let ABC be a triangle,

r

its inradius, and

s

its semiperimeter. Then

area(ABC)=r×s

.

A. Bogomolny, "Relations between Various Elements of a Triangle," Interactive Mathematics Miscellany and Puzzles.

Jay Warendorff, Alexander Bogomolny