Question 17
A more efficient lawn mower is being developed. For this, at a vertex of a square of grass with side $m$, one end of a metal rod of length $p$ is fixed, and at the other end of the rod an equilateral triangle with side $l$ is attached by one of its vertices, where $p+l\lt m$. The triangle spins very fast around its joint with the rod, and the rod rotates very slowly around its joint at the vertex of the square; that is, all the grass under the triangle is cut, forming part of a circular annulus. What is the area that is cut?