Find the area of the quadilateral whose vertices are A (0, 0), B (8, 0), C (3, 4), D (11, 4) ?

  1. 64
  2. 32
  3. 16
  4. None of these

Answer (Detailed Solution Below)

Option 2 : 32
Free
Electric charges and coulomb's law (Basic)
10 Qs. 10 Marks 10 Mins

Detailed Solution

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CONCEPT:

Let A (x1, y1), B (x2, y2) and C (x3, y3) be the vertices of a Δ ABC, then area of Δ ABC = 

CALCULATION:

Given: A (0, 0), B (8, 0), C (3, 4), D (11, 4) 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 (8, 0), C (3, 4) 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 = 

⇒ Area of Δ ABC = 

⇒ Area of Δ ABC = 16 sq. units
 
Similarly, let's find out the area of Δ ACD
 
∵ A (0, 0), C (3, 4) and D (11, 4)
⇒ Area of Δ ACD = 
⇒ Area of Δ ACD = 16 sq units
 
⇒ Area of quadilateral ABCD = Area of ΔABC + Area of Δ ACD = [16 + 16] sq. units = 32 sq. units
 
Hence, option B is the correct answer.

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