UPSC NDA Math Model Paper 9

Given: A (- 3, 1), B (- 1, 4), C (3, 2) and D (1, - 2) are the vertices of a quadilateral ABCD
Here, we have to find the area of quadilateral ABCD
Area of quadilateral ABCD = Area of ΔABC + Area of Δ ACD
Let's find out the area of ΔABC
∵ A (- 3, 1), B (- 1, 4), C (3, 2) are the vertices of ΔABC
As we know that, if A(x1,y1),B(x2,y2) and C(x3,y3) be the vertices of a ΔABC, then area of ΔABC=

1

2

.|

x1	y1	1
x2	y2	1
x3	y3	1

|
⇒ Area of ΔABC=

1

2

.|

−3	1	1
−1	4	1
3	2	1

|
⇒ Area of Δ ABC = 4 sq. units
Similarly, let's find out the area of Δ ACD
∵ A (- 3, 1), C (3, 2) and D (1, - 2)
⇒ Area of ΔACD=

1

2

|

−3	1	1
3	2	1
1	−2	1

|
⇒ Area of Δ ACD = 11 sq. units
⇒ Area of quadilateral ABCD = Area of ΔABC + Area of Δ ACD = (8 + 11) sq. units = 19 sq. units
Hence, option C is the correct answer.