Find the area of the quadrilateral formed by
the points A(-4,2), B(-3,-5), C(3,-2) and D(2,3).
Answers
Answer:
28 sq unit
Step-by-step explanation:
ANSWER
Let the points be A(4,2),B(3,5),C(3,2) and D(2,3)
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, substituting the points (x
1
,y
1
)=(−4,−2) ; (x
2
,y
2
)=(−3,−5) and (x
3
,y
3
)=(3,−2) in the area formula, we get
Area of triangle ABC =
∣
∣
∣
∣
∣
2
(−4)(−5+2)+(−3)(−2+2)+3(−2+5)
∣
∣
∣
∣
∣
=
∣
∣
∣
∣
∣
2
12+0+9
∣
∣
∣
∣
∣
=
2
21
=10.5squnits
And, substituting the points (x
1
,y
1
)=(−4,−2) ; (x
2
,y
2
)=(3,−2) and (x
3
,y
3
)=(2,3) in the area formula, we get
Area of triangle ACD =
∣
∣
∣
∣
∣
2
−4(−2−3)+(3)(3+2)+2(−2+2
∣
∣
∣
∣
∣
=
∣
∣
∣
∣
∣
2
20+