question_answer

In the figure given, area of the shaded region is

A)  1                                            

B)  \[\frac{3}{2}\]

C)  2                                            

D)  \[\frac{5}{2}\]  

Correct Answer: D

Solution :

 Here, we are asked to find the area of the shade dregion, which is difference of areas of two right triangles. Let us redraw the given figure and name the two right - triangles.                 The area of the shaded region can be found by finding the difference of areas of two right tri- angles. In right triangle AOB,                 \[AO=2(2-0)\] and \[OB=3(3-0).\] \[\therefore \]Area of \[AOB=\frac{1}{2}\] (Base) (Height)                 \[=\frac{1}{2}\times (2)\times (3)=3\] In \[\Delta \,COD,\,CO=1(1-0)\] and \[OD=1(1-0)\] \[\therefore \] Area of \[COD=\frac{1}{2}\] (Base) (Height)                 \[=\frac{1}{2}\times (1)\times (1)=\frac{1}{2}\] \[\therefore \] Area of shaded region \[=3-\frac{1}{2}=\frac{5}{2}\]