Here the figure is made up of a quadrilateral and a semi circle.
ABCD is the quadrilateral here. We will find the sides of the quadrilateral by using the distance formula.
If (x₁, y₁) and (x₂, y₂) are two points given, then the distance between two points by using distance formula is,

The co-ordinate of A is (-1,2) and co-ordinate of B is (-2,-1).
So the length of side AB = 
=
(As negative times negative is positive)
= 
The co-ordinate of C is (4,-3) and D is (5,0)
The length of side CD
= 
= 
= 
So the sides AB and CD are equal.
The length of side AD
= 
= 
The length of side BC
= 
= 
= 
So the lengths of the sides AD and BC are equal.
So the quadrilateral is a rectangle whose length is
and width is
.
Area of a rectangle = length × width
= 
= 
=
Now the diameter of the semicircle is the side AD = 
So, the radius of the semi-circle = 
=
= 
=
= 
Area of semi-circle =
, where r is the radius.
= 
= 
= 
=
=
( Approximately taken to the nearest tenth)
Total area of the figure =
= 
We have got the required answer.
Option a is correct here.