question_answer

The sides of a quadrilateral taken in order are 7 cm, 6 cm, 3 cm and 4 cm. The angle between the last two sides is a right angle, find the area of quadrilateral.

A)  \[100\text{ }c{{m}^{2}}\]              

B)  \[6\left( \sqrt{6}-1 \right)\,c{{m}^{2}}\] 

C)  \[6\left( \sqrt{6}+1 \right)\,c{{m}^{2}}\]   

D)  \[255.5\text{ }c{{m}^{2}}\]

Correct Answer: C

Solution :

(c): \[A={{A}_{1}}+{{A}_{2}}:{{A}_{1}}=\frac{1}{2}\times 3\times 4=6\] \[{{A}_{2}}:S=9:(S-a)=4;\,\,(s-b)=2;\,(s-c)=3\] \[{{A}_{2}}:\sqrt{9\times 2\times 3\times 4}=6\sqrt{6}\Rightarrow {{A}_{1}}+{{A}_{2}}\]                         \[=6\sqrt{6}+6=6\left( \sqrt{6}+1 \right)\]