Answer :
Area of polygon ABCD is equal to
2121 sq. units.
Given:-
(−4,5),(0,7),(5,−5) and (−4,2) are the vertices of quadrilateral.
To Find:-
Find the area of the polygon with 4 side .
a polygon is a closed two-dimensional shape having straight line segments. It is not a three-dimensional shape. A polygon does not have any curved surface. A polygon should have at least three sides. Each side of the line segment must intersect with another line segment only at its endpoint. Based on the number of sides of a polygon, we can easily identify the polygon shape.
4 side polygon is quadrilateral
Let us Assume,
A(x 1,y 1)=(−2,5)B(x 2,y 2)=(-2,-1)C(x 3,y 3 )=(7,−1)D(x 4,y 4)=(3,−5)
Let us join AC to form two triangles △ABC and △ACD.
Area of triangle=
21[x 1(y 2 −y 3)+x 2(y 3−y 1 )+x 3(y 1−y 2)]
Then, area of the triangle ABC,
ar(△ABC)=
21∣−2(-1+1)+-2(−1−5)+3(5+1)∣
= 21 [0+12+18]
= 21 [30]
= 630 sq. units [Negative sign will be ignored as area cannot be negative]
Area of the triangle ACD,
ar(△ACD)=
= 21[−4(−5+2)+5(−2−5)−4(5+5)]
= 21[−4(−3)+5(−7)−4]
= 21[12−35−40]
= 21 [−63] [Negative sign will be ignored as area cannot be negative]
= 263 sq. units
ar(ABCD)=ar(ABC)+ar(ACD) = 630 + 263
Hence, area of quadrilateral ABCD is equal to
893 sq. units.
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