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### High School Mathematics - 29.18 Area of a triangle

 To find the area of triangle whose vertices are given. Let A(x1, y1), B(x2, y2) and C(x3, y3) be the vertices of the triangle. From A,B,C draw the perpendiculars AL, BM and CN on the x axis. Area of triangle ABC = area of trap ABML + trap ALNC - trap BMNC = 1/2[MB+LA]ML + 1/2[LA+CN]LN - 1/2[MB+NC]MN = 1/2(y2+y1) (x1-x2) + 1/2(y1+y3)(x3-x1) - 1/2(y2+y3)(x3-x2) = 1/2[x1(y2-y3)+x2(y3-y1)+x3(y1-y2)] Alternatively 1/2 Example: Find the area of triangle whose vertices are (1,3), (2,4) and (5,6) Write out the x terms and y terms as shown. Multiply as shown. Divide the result by 2. 1/2[1x4-2x3+2x6-5x4+5x3-1x6] = -1/2 Changing the sign, the area of the triangle in magnitude is 1/2. Directions: Solve the following.
 Q 1: Find the area of the triangle whose vertices are (4,2), (4,5) and (-2,2).11912 Q 2: Find the area of the triangle whose vertices are (0,0), (-2,3) and (10,7).252215 Q 3: Find the area of the triangle whose vertices are (a,0), (0,b) and (x,y).1/2(bx+ay-ab)1/2(ax+by-bx)1/2(abxy) Q 4: If the centroid of triangle is (1,4) and two of the vertices are (4,-3) and (-9,7), find the area of a triangle.183/223183 Q 5: Find the area of the triangle whose vertices are (-8,-2), (-4,-6) and (-1,5).232528 Q 6: Find the area of the triangle whose vertices are (2,7), (3,-1) and (-5,6).53/455/257/2 Q 7: The area of a triangle having vertices are (15,1), (x,3) and (2,7) is 18 sq.units. Find x.10125 Q 8: Find the area of the triangle whose vertices are (a,bc), (b,ca) and (c,ab).abc/21/2[a2(c-b)+b2(a-c)+c2(b-a)]a2+b2+c2/2 Question 9: This question is available to subscribers only! Question 10: This question is available to subscribers only!