Find the area of quadrilateral whose vertises are (1,2)(3,4)(5,3)
Answers
Answer:
Step-by-step explanation:
Solution
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Correct option is
C
2
11
Let the points be A(1,2),B(6,2),C(5,3) and D(3,4)
The quadrilateral ABCD can be divided into triangles ABC and ACD and hence the area of the quadrilateral is the sum of the areas of the two triangles.
Area of a triangle with vertices (x
1
,y
1
) ; (x
2
,y
2
) and (x
3
,y
3
) is
∣
∣
∣
∣
2
x
1
(y
2
−y
3
)+x
2
(y
3
−y
1
)+x
3
(y
1
−y
2
)
∣
∣
∣
∣
Hence, Area of triangle ABC =
∣
∣
∣
∣
2
(1)(2−3)+(6)(3−2)+5(2−2)
∣
∣
∣
∣
=
∣
∣
∣
2
−1+6
∣
∣
∣
=
2
5
squnits
And, Area of triangle ACD =
∣
∣
∣
∣
2
(1)(3−4)+(5)(4−2)+3(2−3)
∣
∣
∣
∣
=
∣
∣
∣
2
−1+10−3
∣
∣
∣
=
2
6
=3squnits
Hence, Area of quadrilateral =
2
5
+3=
2
11
squnits
Hope it helps
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