question_answer

In the adjoining figure there are four squares (1) with side 11 cm, (2) With side 9 en (3) with side 7 cm and (4) with side 5 cm. (The area of the total dotted region) - (area of the lined region) is equal to (in\[c{{m}^{2}}\])

A)  56                              

B)  64           

C)  78                  

D)  89

Correct Answer: B

Solution :

Let area of cutting part be \[x,\,\,y\]and \[~z\,\,c{{m}^{2}}\] Now, Area of two dotted region \[=\left( {{\left( 11 \right)}^{2}}-x \right)+\left( {{\left( 7 \right)}^{2}}-\left( y+z \right) \right)\] \[121-x+49-y-z=\left( 170-x-y-z \right)\] Now, Area of lined region \[\left( {{\left( 9 \right)}^{2}}-x-y+{{\left( 5 \right)}^{2}}-z \right)=81+25-x-y-z\] \[=106-x-y-z\] \[\therefore \]Required area = Area of dotted region Area of lined region \[=170-106-x-y-z+x+y+z=64\]sq. units