Question

Assertion (A): ABCD is a square. E is mid-point of side AB and F is mid-point of side DC. If DA = 16 cm, the area of triangle COF is 32 cm².

Reason (R): EF is ⊥ to DC and OF = `1/2` EF = `1/2` DA = 8 cm. Area of COF = `1/2` × CF × OF.

Options

• A is true, R is false.

• A is false, R is true.

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

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

Answer 1

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

Explanation:

• Reason (R): In square ABCD, EF connects the mid-points of opposite sides AB and DC, making EF perpendicular to DC and equal in length to side DA (EF = DA = 16 cm). Because the diagonal AC and line segment EF bisect each other at point O, the length of OF is half of EF: OF = `1/2` × 16 = 8 cm. Since F is the mid-point of DC, CF = `1/2 xx "DC" = 1/2 xx 16` = 8 cm. The area of right-angled triangle COF is given by `1/2` × CF × OF = `1/2` × 8 × 8 = 32 cm². Thus, Reason (R) is true.
• Assertion (A): The calculations in Reason (R) directly prove that the area of triangle COF is 32 cm², meaning Assertion (A) is also true and is correctly explained by Reason (R).