A rhombus is a quadrilateral having four equal sides where the opposite sides are parallel and opposite angles are equal. The plural form of a rhombus is rhombi or rhombuses.

Properties

All four sides are equal; in rhombus ABCD, AB = BC = CD = DA

Opposite sides are parallel; so AB ∥ CD and BC ∥ DA

Opposite angles are equal; ∠DAB = ∠BCD and ∠ABC = ∠CDA

The two diagonals are perpendicular and bisect each other at 90°; so AC ⊥ BD

Adjacent angles add up 180°; so ∠DAB +∠ABC = 180°, ∠ABC + ∠BCD = 180°, ∠BCD + ∠CDA = 180°, and ∠CDA + ∠DAB = 180°

Formulas

Area

It is the total space enclosed by the rhombus. The formula is given below:

Area (A) = (d_{1} × d_{2})/2, here d_{1} & d_{2} are the diagonals

Problem: Finding the area of a rhombus when only DIAGONALS are known

Find the area of a rhombus whose diagonals measure 8 cm and 6 cm.

Solution:

As we know, Area (A) = (d_{1} × d_{2})/2, where d_{1} = 8 cm and d_{2} = 6 cm = (8 × 6)/2 cm^{2} = 48/2 cm^{2} = 24 cm^{2}

Problem: Finding the area of a rhombus when BASE and HEIGHT are known

Find the area of a rhombus whose base is 11 cm and height is 8 cm.

Solution:

Here we will use an alternative formula, A = s × h, where s = base and h = height In this rhombus, s = 11 cm and h = 8 cm Since, A = s × h = 11 × 8 cm^{2} = 88 cm^{2}

Perimeter

The total distance covered around the edge of the rhombus. The formula is given below:

Perimeter (P) = 4s, here s = side

Problem: Finding the perimeter of a rhombus when only SIDES are known

Find the perimeter of a rhombus whose sides measure 9 cm each.

Solution:

As we know, Perimeter (P) = 4s,where s = 9 cm = 4 × 9 cm = 36 cm