15. The circle has radius $1 \mathrm{~cm}$. Two vertices of the square lie on the circle. One edge of the square goes through the centre of the circle, as shown.
What is the area of the square?
A $\frac{4}{5} \mathrm{~cm}^{2}$
B $\frac{\pi}{5} \mathrm{~cm}^{2}$
C $1 \mathrm{~cm}^{2}$
D $\frac{\pi}{4} \mathrm{~cm}^{2} \quad$ E $\frac{5}{4} \mathrm{~cm}^{2}$
15. A Let the length of the side of the square be $2 x \mathrm{~cm}$. Then, using Pythagoras' Theorem in the triangle shown, $(2 x)^{2}+x^{2}=1^{2}$. So $4 x^{2}+x^{2}=1$. Therefore $x^{2}=\frac{1}{5}$ and the area of the square is $4 x^{2} \mathrm{~cm}^{2}=\frac{4}{5} \mathrm{~cm}^{2}$.