Question

Assertion: If area of ΔAOD = 18 cm² then area of parallelogram ABCD = 72 cm².

Reason: The diagonals of a parallelogram bisect each other.

Options

• Both A and R are true and R is the correct reason for A.

• Both A and R are true but R is the incorrect reason for A.

• A is true but R is false.

• A is false but R is true.

Answer 1

Both A and R are true but R is the incorrect reason for A.

Explanation:

We are given:

• ΔAOD = 18 cm² in a parallelogram ABCD
• Assertion: Area of ABCD = 72 cm²
• Reason: Diagonals of a parallelogram bisect each other

Step 1: Area relationship between triangle and parallelogram

• Diagonals of a parallelogram divide it into 4 triangles of equal area
• ΔAOD is one of these 4 triangles
• Therefore Area(ABCD) = 4 × Area(AOD) = 4 × 18 = 72 cm²

Step 2: Reason analysis

• Reason states: Diagonals bisect each other
• This is true for all parallelograms
• But the reason for the area calculation is not that the diagonals bisect each other, it is that diagonals divide parallelogram into 4 triangles of equal area

Reason is true, but it is not the correct reason for the assertion

Step 3: Conclusion

• Assertion = True
• Reason = True
• Reason is not correct explanation of Assertion