question_answer

Rectangle ACEG below is divided into 4 parts, BCDX is a square. What is the area of shaded part?

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

B)  \[128\,\,c{{m}^{2}}\]

C)  \[125\,\,c{{m}^{2}}\]                     

D)  \[126\,\,c{{m}^{2}}\]

Correct Answer: B

Solution :

Area of square\[BC\times D=16\,\,c{{m}^{2}}\] \[\therefore \] Side\[=4\,\,cm\] Area of rectangle\[EF\times D=32\,\,c{{m}^{2}}\] \[XD\times XF=32\,\,c{{m}^{2}}\] \[4cm\times XF=32\,\,c{{m}^{2}}\] \[XF=8\,\,cm\] Area of Rectangle ABHX \[=64\,\,c{{m}^{2}}\] \[HX\times BX=64\,\,c{{m}^{2}}\] \[HX\times 4\text{ }cm=64\,\,c{{m}^{2}}\] \[HX=16\,\,cm\] \[\therefore \]Area of shaded portion GF XH\[=HX\times XF\]\[=16\,\,cm\times 8\,\,cm=128\,\,c{{m}^{2}}\]