From a point in the interior of an equilateral triangle, perpendiculars are drawn on the three sides. The lengths of the perpendiculars are 14 𝑐𝑚, 10 𝑐𝑚 and 6 𝑐𝑚. Find the area of the triangle.
Show that the triangle 𝐴𝐵𝐶 is a right-angled triangle; if: 𝐴𝐵 = 9 𝑐𝑚, 𝐵𝐶 = 40 𝑐𝑚 and 𝐴𝐶 = 41 𝑐𝑚.