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A quadrilateral has vertices (1,1) (6,2) (5,5) (3,6). Find the area of the quadrilateral.

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roshan-rox | (Level 1) Valedictorian

Posted June 17, 2013 at 1:27 PM via web

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A quadrilateral has vertices (1,1) (6,2) (5,5) (3,6). Find the area of the quadrilateral.

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted June 17, 2013 at 1:42 PM (Answer #1)

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The quadrilateral has vertices (1,1), (6,2), (5,5) and (3,6). It can be divided into two triangles one made by the points (1,1), (5, 5) and (6,2) and the other by the points (1,1), (5, 5) and (3, 6).

For the triangle made by (1,1), (5, 5) and (6,2), the length of the base is `sqrt((5 - 1)^2 + (5 - 1)^2)` = `sqrt(2*16)` = `4*sqrt 2` . The height is the distance of the point (6, 2) from the line x - y = 0. This is `|6 - 2|/sqrt(1+1)` = `4/sqrt 2` . The area of the triangle is `(1/2)*4*sqrt 2*(4/sqrt 2)` = 8.

Similarly, for the other triangle the length of the base is the same `4*sqrt 2` . The height is `|3 - 6|/sqrt 2 = 3/sqrt 2` . The area of the triangle is `(1/2)*4*sqrt 2*(3/sqrt 2)` = 6

The area of the quadrilateral is 14 square units.

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