question_answer

ABCD is a parallelogram X and Y are the mid points of sides BC and CD respectively. If the area of \[\Delta \,\mathbf{ABC}\] is 16\[\mathbf{c}{{\mathbf{m}}^{\mathbf{2}}}\], then the area of \[\Delta \mathbf{AXY}\]is

A)  12 \[c{{m}^{2}}\]

B)  8 \[c{{m}^{2}}\]

C)  9 \[c{{m}^{2}}\]                                

D)  10 \[c{{m}^{2}}\]

Correct Answer: A

Solution :

(a):             \[\Delta AXY=\frac{3}{8}([\,\,\,]\,ABCD)\] \[=\frac{3}{4}\Delta ABC\] \[=\frac{3}{4}\times 16=12\] sq.cm.