# Rhombus

## Definition

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

1. All four sides are equal; in rhombus ABCD, AB = BC = CD = DA
2. Opposite sides are parallel; so AB ∥ CD and BC ∥ DA
3. Opposite angles are equal; ∠DAB = ∠BCD and ∠ABC = ∠CDA
4. The two diagonals are perpendicular and bisect each other at 90°; so AC ⊥ BD
5. 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) = (d1 × d2)/2, here d1 & d2 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) = (d1 × d2)/2, where d1 = 8 cm and d2 = 6 cm
= (8 × 6)/2 cm2
= 48/2 cm2
= 24 cm2

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 cm2
= 88 cm2

### 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

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