The distance between two sides AB and DC of rhombus ABCD is PQ and distance between sides AD and BC is RS; let’s prove that PQ = RS.

Given.

The distance between two sides AB and DC of rhombus ABCD is PQ and distance between sides AD and BC is RS

Formula used.

Opposite sides of rhombus are parallel

And all sides of are equal in rhombus

Area of triangle = × Base × Height

Draw Δ DPC by joining DP and PC and

Δ CRB by joining CR and RB in rhombus

In triangle DPC and rhombus ABCD

Both lies on same base CD

And lies between parallel lines AB || CD

⇒ Because opposite sides of rhombus are parallel

∴ Area of Rhombus ABCD = × Area of triangle DPC

In triangle CRB and rhombus ABCD

Both lies on same base BC

And lies between parallel lines BC || AD

⇒ Because opposite sides of rhombus are parallel

∴ Area of Rhombus ABCD = × Area of triangle CRB

By equating both

Area of triangle DPC = Area of triangle CRB

× PQ × CD = × RS × BC

As all sides of rhombus are equal

⇒ CD = BC

× PQ × CD = × RS × CD

∴ PQ = RS

Hence proved ;