question_answer

Area of quadrilateral formed by the vertices (- 1, 6), (-3, -9), (5, -8) and (3, 9) is ____ sq.

A)  96         

B)  18             

C)  50                               

D)  25

Correct Answer: A

Solution :

(a): Divide into two triangles and find area and apply Heron?s formula: Ailter: (Aliter means ?alternate method?) Heron?s formula requires lot of calculations, that too in square roots. So, this is proto calculation mistakes. If we can draw the points in coordinate axes, we get sum areas of three \[\Delta s\].             \[Area=\,area\,(\Delta \,A+\Delta \,B+\Delta \,C)\] \[=\frac{1}{2}\times 6\times 15+\frac{1}{2}\times 4\times 17+\frac{1}{2}\times 2\times 17=96\]