<prompt> Fumana sebaka sa kgutlotharo seo dinoko tsa sona e leng 1,1, 6,-2, 1,4.nan  <response>: Instruction in English: Find the area of the triangle whose vertices are 1,1, 6,-2, 1,4. . Response in English: We can use the Shoelace Formula or Gausss area formula to find the area of the triangle. The formula states that the area of a simple polygon whose n vertices are defined by the coordinates x1, y1, x2, y2, ..., xn, yn is given by the following expression: A 12 x1y2 x2y3 ... xn-1 yn xny1 - y1x2 - y2x3 - ... - yn-1 xn - ynx1.Applying this formula to the given problem, we have that the area of the triangle whose vertices are 1,1, 6,-2, 1,4 is given by:A 12 1-2 64 1-1 - -16 - -21 - 41 12 -2 24 -1 6 2 - 4 12 25 12.5Therefore, the area of the triangle is 12.5 square units. . Response in Sesotho: Re ka sebelisa Foromo ea Shoelace kapa foromo ea sebaka sa Gauss ho fumana sebaka sa kgutlotharo. Foromo e bolela hore sebaka sa polygon e bonolo eo li-n vertices li hlalosoang ke likhokahano x1, y1, x2, y2, ..., xn, yn e fanoa ke polelo e latelang: A 1 2 x1y2 x2y3 ... xn-1 yn xny1 - y1x2 - y2x3 - ... - yn-1 xn - ynx1. Ha re sebelisa foromo ena bothateng bo fanoeng, re na le hore sebaka sa kgutlotharo seo dinoko tsa sona e leng 1,1, 6,-2, 1,4 se fanoeng ke: A 12 1 -2 6 4 1-1 - -1 6 - -2 1 - 4 1 12 -2 24 -1 6 2 - 4 12 25 12.5 Ka hona, sebaka sa kgutlotharo ke 12.5 lisekoere diyuniti. 