What is the area of quadrilateral ABCD?

Given:

• A quadrilateral ABCD, and
• AD = l and DC = w

To find:

• The area of the quadrilateral, ABCD

Analysing Statement 1
“\(l^2 + 2lw + w^2 = 16\)”

• Implies, l + w = 4

However, we cannot infer anything about the other two sides of the quadrilateral.

So, we cannot find the area of ABCD

Therefore, Statement 1 is NOT sufficient to arrive at a unique answer

Analysing Statement 2
“\(l^2 - 2lw + w^2 = 4\)”

• Implies, l – w = 2

However, we cannot infer anything about the other two sides of the quadrilateral.

So, we cannot find the area of ABCD

Therefore, Statement 2 is NOT sufficient to arrive at a unique answer

Combining Both Statements

• From Statement 1, we know, l + w = 4
• From Statement 2, we know, l - w = 2
• Solving the above equations, we get, l = 3 and w = 1

However, we cannot infer anything about the other two sides of the quadrilateral.

So, we cannot find the area of ABCD

Therefore, both statements TOGETHER are NOT sufficient to arrive at a unique answer

Hence, the correct answer is option E.

Answer: E