Find the area of quadrilateral ABCD whose vertices are A(-3,-3),B(2,-3),C(2,3),D(-1,2)
Answers
Answer:
28 sq. units
Step-by-step explanation:
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Maths
Heron's Formula
Area of Quadrilateral
Find the area of the quadri...
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Asked on December 27, 2019 by
Ashesh Kosambia
Find the area of the quadrilateral ABCD, whose vertices are A(−3,−1),B(−2,−4),C(4,−1) and D(3,4).
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ANSWER
The coordinates of ABCD are A(−3,−1),B(−2,−4),C(4,−1),D(3,4).
Area of quadrilateral ABCD = Area of triangle ABC + Area of triangle ACD
Area of triangle =
2
1
∣[x
1
(y
2
−y
3
)+x
2
(y
3
−y
1
)+x
3
(y
1
−y
2
)]∣
Area of triangle ABC =
2
1
∣[−3(−4+1)−2(−1+1)+4(−1+4)]∣
=
2
1
∣[9+12]∣=
2
21
sq. units
Area of triangle ACD =
2
1
∣[−3(−1−4)+4(4+1)+3(−1+1)]∣
=
2
1
∣[15+20]∣=
2
35
sq. units
Therefore, Area of quadrilateral ABCD =
2
21
+
2
35
=28 sq. units