is this quadrilateral a parallelogram?If yes, state the definition or theorem that justifies your answer.
2 answers:
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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.
