UPSC NDA Math Model Paper 6

Given: A (0, 0), B (0, 10), C (8, 2) and D (8, 7) 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 (0, 0), B (0, 10), C (8, 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 Δ ABC, then area of Δ ABC =

1

2

.|

x1	y1	1
x2	y2	1
x3	y3	1

| ⇒ Area of ΔABC=

1

2

.|

0	0	1
0	10	1
8	2	1

|
⇒ Area of ΔABC=40sq. units
Similarly, let's find out the area of ΔACD
∵A(0,0),C(8,2) and D(8,7)
⇒ Area of ΔACD=

1

2

.|

0	0	1
8	2	1
8	7	1

|
⇒ Area of Δ ACD = 20 sq units
⇒ Area of quadilateral ABCD = Area of ΔABC + Area of Δ ACD = [40 + 20] sq. units = 60 sq. units
Hence, option C is the correct answer.