Mathematics
Assertion (A): PQRS a parallelogram whose area is 180 cm2 and A is any point on the diagonal PR. The area of triangle ASR = 30 cm2.
Reason (R): A is not the mid-point of diagonal PR.
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,
Area of parallelogram PQRS = 180 cm2.
We know that,
Diagonal of a parallelogram divides it into two triangles of equal area.
So, area of ΔPRS = = 90 cm2
Now, A is any point on PR.
So, area of ΔASR < area of ΔPRS.
i.e., area of ΔASR < 90 cm2.
But the area of triangle ASR = 30 cm2 is not necessarily true based solely on the fact that A is any point on PR.
∴ Assertion (A) is false.
From figure,
A does not lies on the diagonal QS.
Since, diagonals of || gm bisect each other.
Thus, A is not the mid-point of diagonal PR.
∴ Reason (R) is true.
∴ A is false, but R is true.
Hence, option 2 is the correct option.
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