The area of a rectangle can be found when we know the lengths of its sides. Is the same true Class 9

The area of a rectangle can be found when we know the lengths of its sides. Is the same true Class 9

Question 1.

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? Class 9

Answer:

No, we cannot find the area of a parallelogram from its side lengths alone.

When we keep the side lengths fixed but change the angle between adjacent sides:

1. As the angle increases toward 90°, the height increases

∴ area increases

1. As the angle decreases toward 0°, the height decreases

∴ area decreases

So, the same pair of side lengths gives different areas at different angles.

This shows that side lengths alone are not enough, we also need either the height or the angle between the sides to