Question

A dart is thrown and hits the square target in the diagram...

Answer 1

R - radius of a circle
d - diagonal of a square inscribed in a circle
a - side of a square inscribed in a circle
shaded area - area of a square inscribed in a circle

$A_{circle}=r^2\pi \\d=2r=a \sqrt{2} \\ \\a= \frac{2r}{ \sqrt{2} } =r \sqrt{2} \\ \\A_{square}=a^2=(r \sqrt{2} )^2=2r^2 \\ \\P= \frac{A_{square}}{A_{circle}} = \frac{2r^2}{r^2\pi}= \frac{2}{\pi}\approx0.64\times 100\%=64\%$