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 \[=3-\frac{1}{2}=\frac{5}{2}\]You need to login to perform this action.
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