question_answer

P and Q are the midpoints of the side AB and AC , respectively of a triangle ABC. The ratio of the y area of the trapezium PQCB to the area of the triangle APQ is

A)  1                            

B)         2

C)  3                                              

D)  4

Correct Answer: C

Solution :

 Let EC = a, then \[PQ=\frac{a}{2}.\] BC and PQ are parallel. Also \[AD=DE=h,\] say \[\therefore \] Area of \[\Delta \,APQ=\frac{1}{2}\times PQ\times AD=\frac{ah}{4}\] and Area of trapezium PQCB \[=\frac{1}{2}\times DE\times (BC+PQ)\] \[=\frac{1}{2}h\left( a+\frac{a}{2} \right)=3\times \frac{ah}{4}\] \[=3\times \] Area of \[\Delta \,APQ\]