question_answer

An area of the quadrilateral whose sides measure 9 cm, 40 cm, 28 cm and 15 cm and in which the angle between the first two sides is a right angle is

A)  \[206\,\,c{{m}^{2}}\]             

B)  \[306\,\,c{{m}^{2}}\]

C)  \[356\,\,c{{m}^{2}}\]             

D)  \[380\,\,c{{m}^{2}}\]

Correct Answer: B

Solution :

Applying Pythagoras theorem in\[\Delta ABC,\]we get \[{{9}^{2}}+{{40}^{2}}=A{{C}^{2}}\] \[\Rightarrow \]   \[AC=\sqrt{1681}=41\,\,cm\] \[\therefore \]Area of quadrilateral = Area of \[\Delta ABC+\] Area of \[\Delta ADC\] \[=\frac{1}{2}(9\times 40)+\sqrt{42\times 1\times 14\times 27}\] \[=180+14\times 3\times 3=180+126=306\,\,c{{m}^{2}}\]