Discover the flexible properties of parallelograms. Learn how their instability makes them useful for adjustable mechanisms and engineering applications.
A parallelogram is a quadrilateral where two pairs of opposite sides are parallel. This simple requirement leads to many interesting properties and practical applications.
Unlike triangles, parallelograms are structurally unstable - they can be deformed without changing side lengths, which makes them useful for adjustable mechanisms.
Two pairs of parallel sides
Parallel sides have equal length
But not necessarily 90°
Cross at their midpoints
P = 2 × (a + b)
Where a and b are adjacent side lengths
Example: Sides 8 and 5 → P = 2 × (8 + 5) = 26 units
A = b × h
Where b is base length and h is perpendicular height
Example: Base 8, height 4 → A = 8 × 4 = 32 square units
Unlike triangles, parallelograms can be deformed without changing side lengths
This instability is actually useful for adjustable mechanisms and folding structures
Forces applied to parallelograms are distributed across parallel members
Students often multiply two adjacent sides instead of using base × height.
✅ Solution: Remember: Area = base × perpendicular height, NOT side × side.
The height is perpendicular to the base, not the slanted side length.
✅ Solution: Always identify which measurement is the perpendicular height versus the slanted side.
Students sometimes apply rectangle properties to general parallelograms.
✅ Solution: Only rectangles have right angles; general parallelograms have opposite angles equal but not necessarily 90°.
Collapsible clothing racks use parallelogram structures that can expand and contract while maintaining parallel bars.
Industrial scissor lifts use multiple parallelograms to raise and lower platforms while keeping them level.
Articulated desk lamps use parallelogram linkages to maintain light orientation as the arm moves.
Test your understanding with interactive parallelogram calculators and problem-solving tools.