Rhombus Problems
Rhombus problems with detailed solutions.
Definition of a RhombusThe rhombus is a parallelogram with four congruent sides. A square is a special case of a rhombus.
Properties of a RhombusThese 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 RhombusThese are three formulas for the area of the rhombus.Formula 1area = 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 2area = a^{ 2} sin (A) = a^{ 2} sin (B). Since angles A and B are supplementary angles, sin (A) = sin (B).Formula 3area = (1/2) d1 d2, where d1 and d2 are the lengths of the two diagonals.
Problems with Detailed SolutionsProblem 1The 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 its area. Solution to Problem 1:
Problem 2The lengths of the diagonals of a rhombus are 20 and 48 meters. Find the perimeter of the rhombus? Solution to Problem 2:
Problem 3The 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 GeometryGeometry Tutorials, Problems and Interactive Applets.Rhombus - Geometry Calculator to calculate the characteristics of a rhombus |