Circle Areas #1: The Basics

If you look closely, you'll see that $\{3, 4, 5\}$ is a Pythagorean triple. Thus this triangle is right, i.e. $3^2+4^2=5^2$ . The triangle has an area of $\dfrac{3\times4}{2}=6$ . The semiperimeter can be found as:

$\dfrac{3+4+5}{2}=6$

Using our formula for area, i.e. $A=rs$ where $r$ is the inradius and $s$ is the semiperimeter, we can write:

$6=6r$

Thus the inradius has length $1$ . So the area is $1^2\pi$ and the constant $a=1^2=\boxed{1}$ .

A=(rp)/2 Where r = radius, p= perimeter and A= area of triangle

area of triangle = (3*4)/2 =6 p =3+4+5 = 12 p=12

6=(r12)/2 6r=6 r=1

r^1 * pi = area of circle 1pi= area of circle

a=1

By using Heron's Formula; Any circle inscribed in a triangle know of lengths of its sides we can get the radius by: Area of the triangle divided by half the perimeter: Half the Perimeter of the triangle = (3+4+5)/2 = 6 cm

Area of the triangle = sqrt [ 6 (6-3) (6-4) (6-5) ] = 6 cm^2

The radius = 6/6 = 1 cm