Use the following information to answer the next question.

The given figure shows a quadrilateral ABCD with its dimensions. It is given that the perimeter ofΔACD is 96 cm, while that of ΔABC is 240 cm.

What is the area of quadrilateral ABCD?

 

• A) 

  384 cm²

• B) 

  1536 cm²

• C) 

  1920 cm²

• D) 

  2304 cm²

 Answer:DSolution:

Perimeter of ΔACD = 96 cm

∴ AC + CD + DA = 96 cm

⇒ AC + 32 cm + 24 cm = 96 cm

⇒ AC + 56 cm = 96 cm

⇒ AC = 96 cm – 56 cm = 40 cm

Perimeter of ΔABC = 240 cm

∴ AB + BC + AC = 240 cm

⇒ AB + 96 cm + 40 cm = 240 cm

⇒ AB + 136 cm = 240 cm

⇒ AB = 240 cm – 136 cm = 104 cm

Semi-perimeter of ΔACD

Similarly, semi-perimeter of ΔABC = 120 cm

∴ Area of ΔACD

Simialrly, area of ΔABC

∴ Area of quadrilateral ABCD = Area of ΔACD + Area of ΔABC

The correct answer is D.

If we apply Brahmagupta formula i.e Sq root of (S-a)(s-b)(S-c)(s-d) the answer is different  .  Pl explain why it is so.  My answer is 768x Sq rt 13.