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  • Draw a quadrilateral in the Cartesian plane, whose vertices are (– 4, 5), (0, 7), (5, – 5) and (– 4, –2). Also, find its area.

Q : 1     Draw a quadrilateral in the Cartesian plane, whose vertices are (-4,5),(0,7),(5,-5)  and  (-4,-2). Also, find its area. 

Answers (1)

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Area of ABCD = Area of ABC + Area of ACD
Now, we know that the area of a triangle with vertices (x_1,y_1),(x_2,y_2) \ and \ (x_3,y_3)  is given by
A = \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|
Therefore,
Area of triangle ABC = \frac{1}{2}|-4(7+5)+0(-5-5)+5(5-7)|= \frac{1}{2}|-48-10|= \frac{58}{2}=29
Similarly,
Area of triangle ACD = \frac{1}{2}|-4(-5+2)+5(-2-5)+-4(5+5)|= \frac{1}{2}|12-35-40|= \frac{63}{2}
Now,
Area of ABCD = Area of ABC + Area of ACD
                        =29+\frac{63}{2}
                        =\frac{121}{2} \ units

 

Posted by

Gautam harsolia

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