NCERT Solutions for Class 9th Maths Chapter 6 Think and Reflect — Area of a Parallelogram
Book page 131–132 Updated on2026-09-08
Q1.
The area of a rectangle can be found when we know the lengths of its sides. Is the same true for a parallelogram? That is, can we find the area of a parallelogram when we know the lengths of its sides? Why or why not? (Hint: What happens to the area of a parallelogram if we decrease or increase the angle between the adjacent sides while keeping the lengths fixed?)
Answer
No. The side lengths do not determine the area of a parallelogram. Two parallelograms can have exactly the same four sides and completely different areas.
Same sides, different angles — and so a smaller height and a smaller area. Only the angle has changed.
Area = base × height = b × h The base b is fixed by the side length, but h is not. As the angle between the sides is squeezed towards 0°, h → 0 and the area → 0. As the angle opens towards 90°, h grows to its maximum, the other side length a.
So for fixed sides a and b: 0 < area ≤ ab, with equality only for a rectangle.
Why it happens: a parallelogram made of four rods hinged at the corners is a flexible figure — you can push it flat without changing any side. A triangle made of three rods cannot be flexed at all, which is why three sides do determine a triangle's area (Heron's formula) but four sides never determine a 4-gon's area. The book makes exactly this point again with the rhombus of sides 3, 3, 3, 3 in Fig. 6.27, whose area can be 9, or 8.01, or 5.41.
Did you know? This is why builders put a diagonal brace across a gate. The four sides alone leave the gate free to sag into a thin parallelogram; the diagonal turns it into two rigid triangles.