Rhombus Problems

Rhombus problems with detailed solutions are presented. Rhombus Calculator and Solver also included.

Definition of a Rhombus

The rhombus is a parallelogram with four congruent sides (sides with equal lengths). A square is a special case of a rhombus.
rhombus

Properties of a Rhombus

These are some of the most important properties of a rhombus.
Consider the rhombus ABCD shown in the figure above.
1 - All sides are congruent (equal lengths).
length AB = length BC = length CD = length DA = a.
2 - Opposite sides are parallel.
AD is parallel to BC and AB is parallel to DC.
3 - The two diagonals are perpendicular.
AC is perpendicular to BD.
4 - Opposite internal angles are congruent (equal sizes).
internal angle A = internal angle C
and
internal angle B = internal angle D.
5 - Any two consecutive internal angles are supplementary : they add up to 180 degrees.
angle A + angle B = 180 degrees
angle B + angle C = 180 degrees
angle C + angle D = 180 degrees
angle D + angle A = 180 degrees

Area of a Rhombus

These are three formulas for the area of the rhombus.

Formula 1

area = a × h , where a is the side length of the rhombus and h is the perpendicular distance between two parallel sides of the rhombus.

Formula 2

area = a 2 sin (A) = a 2 sin (B). Since angles A and B are supplementary angles, sin (A) = sin (B).

Formula 3

area = (1/2) d1 d2, where d1 and d2 are the lengths of the two diagonals.

Problems on Rhombus with Detailed Solutions

Problem 1

The size of the obtuse angle of a rhombus is twice the size of its acute angle. The side length of the rhombus is equal to 10 feet. Find the area of the rhombus.

Solution to Problem 1:

Problem 2

The lengths of the diagonals of a rhombus are 20 and 48 meters. Find the perimeter of the rhombus.
Solution to Problem 2:

Problem 3

The perimeter of a rhombus is 120 feet and one of its diagonal has a length of 40 feet. Find the area of the rhombus.

Solution to Problem 3:

More References and Links to Geometry

Geometry Tutorials, Problems and Interactive Applets.
Rhombus - Geometry Calculator to calculate the characteristics of a rhombus