Q2 of 184 Page 10

Find the area of the quadrilateral whose vertices are

Given (1, 0), (5, 3), (2, 7) and (-2, 4)


To Find: Find the area of the quadrilateral.


Let us Assume A(x1, y1) = (1, 0)


Let us Assume B(x2, y2) = (5, 3)


Let us Assume C(x3, y3) = (2, 7)


Let us Assume D(x4, y4) = (-2, 4)


Let us join Ac to from two triangles ∆ABC and ∆ACD


Now


Area of triangle


Then,


Area of given triangle ABC




Square units


Area of given triangle ABC




square units


Area of quadrilateral ABCD = Area of ABC + Area of ACD



Hence, Area = 25 sq units.


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2

Find the area of the quadrilateral whose vertices are

Given (-5, 7), (-4, -5), (-1, -6) and (4, 5)

 2

Find the area of the quadrilateral whose vertices are

Given (0, 0), (6, 0), (4, 3), and (0, 3)

 3

Find the area of the quadrilateral whose vertices taken in order are (- 4, -2), (-3, -5), (3, -2) and (2, 3).

 4

A median of a triangle divides it into two triangles of equal area. Verify this result for ABC whose vertices are A(1, 2), B(2, 5), C(3, 1).