Question 1201695
<font color=black size=3>
The square has area 70 square cm.
The side length is {{{sqrt(70)}}} cm.


{{{
drawing(400,400,-4,4,-4,4,
circle(0,0,3),
line(-2.12,2.12,2.12,2.12),line(2.12,2.12,2.12,-2.12),line(2.12,-2.12,-2.12,-2.12),line(-2.12,-2.12,-2.12,2.12),line(-2.12,-2.12,2.12,2.12),
circle(0,0,0.0412),circle(0,0,0.0824),circle(0,0,0.1236),
locate(0.86,1.36,"r"),locate(-1.26,-0.56,"r"),
locate(-2.74,0.2,sqrt(70)),locate(-0.36,2.68,sqrt(70))
)
}}}
For each right triangle, the hypotenuse is the diameter of the circle.
r = radius
2r = diameter = hypotenuse
Use the pythagorean theorem to find that {{{hypotenuse = 2r = sqrt(140)}}}
Or you could use the 45-45-90 triangle template to connect the leg length to the hypotenuse.
{{{matrix(1,3,hypotenuse=(matrix(1,2,leg,length))*sqrt(2), "", matrix(1,4,only,for,45-45-90,triangles))}}}


Then it leads to
{{{r = sqrt(140)/2}}}


The area of the circle is then...
{{{A = pi*r^2}}}


{{{A = pi*(sqrt(140)/2)^2}}}


{{{A = pi*(((sqrt(140))^2)/(2^2))}}}


{{{A = pi*(140/4)}}}


{{{A = pi*35}}}


{{{A = 35pi}}}


The exact area of the circle is 35pi square cm.


If you use the approximation pi = 3.14, then the approximate area of the circle would be 35*pi = 35*3.14 = 109.9 square cm.
</font>