Example 15 - Chapter 7 Class 10 Coordinate Geometry
Last updated at May 29, 2018 by Teachoo
Last updated at May 29, 2018 by Teachoo
Transcript
Example 15 If A( 5, 7), B( 4, 5), C( 1, 6) and D(4, 5) are the vertices of a quadrilateral, find the area of the quadrilateral ABCD. Let the vertices of quadrilateral be A( 5, 7) , B( 4, 5) C( 1, 6) , D(4, 5) Joining AC, There are 2 triangles formed ABC & ACD Hence, Area of quadrilateral ABCD = Area of ABC + Area of ADC Finding area ABC Area of triangle ABC = 1/2 [ x1(y2 y3) + x2(y3 y1) + x3(y1 y2) ] Here x1 = 5 , y1 = 7 x2 = 4 , y2 = 5 x3 = 1 , y3 = 6 Putting values Area of triangle ABC = 1/2 [ 5( 5 ( 6)) + ( 4)( 6 7) + ( 1)(7 ( 5)) ] = 1/2 [ 5( 5 + 6) 4( 13) + ( 1)(7 + 5)] = 1/2 [ 5(1) 4( 13) + ( 1)(12)] = 1/2 [ 5 + 52 12] = 1/2 [35] square units Similarly, Finding area ADC Area of triangle ADC = 1/2 [ x1(y2 y3) + x2(y3 y1) + x3(y1 y2) ] Here x1 = 5 , y1 = 7 x2 = 4 , y2 = 5 x3 = 1 , y3 = 6 Area of triangle ADC = 1/2 [ 5(5 ( 6)) + 4( 6 7) + ( 1)(7 5) ] = 1/2 [ 5(5 + 6) + 4( 13) + ( 1)(2)] = 1/2 [ 5(11) + 4( 13) + ( 1)(2)] = 1/2 [ 55 52 2] = 1/2 [ 109] But area cannot be negative, So, Area of triangle ADC = 1/2 [ 109] square units Area of quadrilateral ABCD = Area of triangle ABC + Area of triangle ADC = 1/2 [ 35 + 109] = 1/2 [ 144] = 72 square units
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