Question

If PQRS is a parallelogram whose area is 180 cm² and A is any point on the diagonal QS, then ar(ΔASR) is _______ 90 cm²?

Answer 1

Given:
PQRS is a parallelogram with area 180 cm²
A is any point on the diagonal QS


We know, the diagonal of the parallelogram bisects it into two triangles of equal area.
Thus, ar(ΔPQS) = ar(ΔQRS) = $\frac{1}{2}$ar(PQRS)
⇒ ar(ΔPQS) = ar(ΔQRS) = 90 cm²

Therefore, ar(ΔASR) is always less than 90 cm² unless or until the point A coincides with Q or S.

Hence, ar(ΔASR) is less than 90 cm²