Mathematics - Straight Lines Question with Solution | TestHub

Set $B=(0,0),C=(a,0),A=(\frac{a}{2},\frac{\sqrt{3}a}{2})$. Bisectors of an equilateral triangle are its medians. In the chamber bounded by BC and the medians from A and C, for $P=(x,y)$ the condition is $\min \left(x-\frac{a}{2},\frac{a-x-\sqrt{3}y}{2}\right)<y$, cutting off two triangles of total area $\frac{(3-\sqrt{3})a^2}{48}$ per chamber. Required area $=\frac{\sqrt{3}{a}^2}{4}-6\cdot \frac{(3-\sqrt{3})a^2}{48}=\frac{3(\sqrt{3}-1)a^2}{8}$ Answer: Option B.