
The area of the pentagon whose vertices are (4,1), (3,6), (-5,1), (-3,-3) and (-3,0) is
A.30 sq. units
B.60 sq. units
C.120 sq. units
D.None of these
Answer
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Hint: We are given the coordinates of all the five points, we use the formula of area of pentagon which is
Area of the pentagon ; where n = 1, 2, 3, 4, 5. We substitute the values and find the area.
Complete step-by-step answer:
Pentagon is a plane figure with five straight sides and five angles.
Here, the given vertices are (4,1), (3,6), (-5,1), (-3,-3) and (-3,0).
Now, Let,
=(4,1)
=(3,6)
=(-5,1)
=(-3,-3)
=(-3,0)
Now, apply the formula of area of a pentagon, which is
; where n = 1, 2, 3, 4, 5
Putting the values of xi and yi where i = 1, 2, 3, 4, 5 in the formula we get
Hence, the area of the pentagon is 30 sq. units .
Hence, the correct option is (A).
Note: 1. A pentagon is any five –sided polygon. Sometimes it is called 5-gon. The sum of the angles in a simple pentagon is .
2.The formula given below is also valid for all polygons ,
Area of the pentagon
Complete step-by-step answer:
Pentagon is a plane figure with five straight sides and five angles.
Here, the given vertices are (4,1), (3,6), (-5,1), (-3,-3) and (-3,0).

Now, Let,
Now, apply the formula of area of a pentagon, which is
Putting the values of xi and yi where i = 1, 2, 3, 4, 5 in the formula we get
Hence, the area of the pentagon is 30 sq. units .
Hence, the correct option is (A).
Note: 1. A pentagon is any five –sided polygon. Sometimes it is called 5-gon. The sum of the angles in a simple pentagon is
2.The formula given below is also valid for all polygons ,
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