question_answer

The adjacent sides of a parallelogram are 8 cm and 9 cm. The diagonal joining the ends of these sides is 13 cm. Its area is

A)  \[75%\]                      

B)  \[120%\]

C)  \[8m\times 6m\]        

D)  \[\frac{5}{2}(9+5\sqrt{3})sq.cm\]

Correct Answer: B

Solution :

As shown in the diagram, area of triangle ABC = 1/2 area of the parallelogram ABCD. By Heron's formula, area of triangle \[\Delta BCD\] Here \[=\left( \frac{1}{2}\times BD\times AL \right)+\left( \frac{1}{2}\times BD\times CM \right)\] \[=\frac{1}{2}\times BD\times (AL+CM)\] Area of \[=b\times h\] \[\frac{2\pi rh}{\pi r}=\frac{8}{5}\] Hence, area of \[:h=5:4\]