<prompt> Bala sebaka sa trapezoid e nang le likhokahano tsa vertex A-2, 5, B-7, 9, C-1, 13, le D-3, 10.nan  <response>: Instruction in English: Calculate the area of a trapezoid with vertex coordinates A-2, 5, B-7, 9, C-1, 13, and D-3, 10. . Response in English: To solve this problem, I can use the formula for the area of a trapezoid: Area h2a b, where h is the height, a and b are the lengths of the parallel sides.Lets start by finding the lengths of the parallel sides: Side AB is parallel to side CD. To find their lengths I can use the distance formula:AB -7--22 9-52 5242 52CD -1--32 13-102 2232 13Now lets calculate the height of the trapezoid. The height is the perpendicular distance between the parallel sides. To find the height, I can use the point-to-line distance formula to find the perpendicular distance from point D-3, 10 to line AB.First, lets find the equation of line AB:The slope of line AB is m 9 - 5-7 - -2 4-5 -45. The equation of line AB is y - 5 -45x 2, which can be rearranged to the standard form: 4x 5y 5.Now lets find the distance from point D-3, 10 to line AB. Using the point-to-line distance formula, we have:Distance 4-3 510 - 5 42 52 4141Finally, lets find the area of the trapezoid using the formula: Area h2a bArea 41241 52 13Area 18.6435 square unitsSo, the area of the trapezoid with vertex coordinates A-2, 5, B-7, 9, C-1, 13, and D-3, 10 is approximately 18.64 square units. . Response in Sesotho: Ho rarolla bothata bona, nka sebelisa mokhoa oa sebaka sa trapezoid: Sebaka h2 a b, moo h e leng bophahamo, a le b ke bolelele ba mahlakore a tšoanang. Ha re qaleng ka ho fumana bolelele ba mahlakore a bapileng: Lehlakoreng la AB le bapile CD ea lehlakore. Ho fumana bolelele ba tsona nka sebelisa mokhoa oa sebaka: AB -7--22 9-52 5242 52 CD -- 1--32 13-102 2232 13 Joale ha re bale bolelele ba trapezoid. Bophahamo ke sebaka sa perpendicular pakeng tsa mahlakore a bapileng. Ho fumana bophahamo, nka sebelisa mokhoa oa sebaka sa ntlha-to-line ho fumana sebaka sa perpendicular ho tloha ntlha ea D -3, 10 ho ea ho AB. Pele, a re fumaneng equation ea mola AB: Moepa oa mola AB ke m 9 - 5-7 - -2 4-5 -45. Equation ea mola AB ke y - 5 -45 x 2, e ka hlophisoa bocha ho ea ka mokhoa o tloaelehileng: 4x 5y 5. Joale a re fumane sebaka ho tloha ntlha ea D-3, 10 ho latela AB. Re sebelisa mokhoa oa ho tloha ho ntlha ho ea ho mola, re na le: Distance 4 -3 510 - 5 42 52 4141 Qetellong, a re fumaneng sebaka sa trapezoid re sebelisa foromo: Sebaka h2a b Sebaka 41241 5 2 13 Sebaka 18.6435 li-square units Kahoo, sebaka sa trapezoid se nang le vertex coordinates A -2, 5, B -7, 9, C -1, 13, le D -3, 10 e batla e le 18.64 square units. 