Mathematics
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 = DA = 8 cm.
Area of COF = x CF x OF
A is true, but R is false.
A is false, but 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.
Theorems on Area
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Answer
Given, ABCD is a square. DA = 16 cm.
∴ AB = BC = CD = DA = 16 cm
F is mid-point of DC.
CF = x DC = x 16 = 8 cm.
If EF is ⊥ to DC, then OF is perpendicular to DC.
Area of ΔCOF = x base x height
= x CF x OF
= x 8 x 8
= 4 x 8
= 32 cm2.
∴ Both A and R are true, and R is the correct reason for A.
Hence, option 3 is the correct option.
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