a square is a rhombus with all angles congruent

Rhomb Problems

Rhombus problems with elaborated solutions are given. Rhomb Calculator and Problem solver also included.

Definition of a Rhomb

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

Properties of a Rhomb

These are just about of the most evidentiary properties of a rhomb.
Consider the rhombus ABCD shown in the figure above.
1 - All sides are identical (equal lengths).
distance AB = duration BC = length Four hundred = length DA = a.
2 - Opposite sides are parallel.
Anno Domini is parallel to BC and Abdominal muscle is parallel to DC.
3 - The cardinal diagonals are perpendicular.
AC is unsloped to BD.
4 - Opposite internal angles are congruent (equal sizes).
internal angle A = internal angle C
and
interior angle B = interior angle D.
5 - Any two consecutive internal angles are supplementary : they summate to 180 degrees.
angle A + angle B = 180 degrees
angle B + angle C = 180 degrees
angle C + lean D = 180 degrees
angle D + tip over A = 180 degrees

Area of a Rhombus

These are three formulas for the surface area of the rhombus.

Formula 1

area = a � h , where a is the side distance of the rhombus and h is the perpendicular aloofness betwixt two parallel sides of the rhombus.

Formula 2

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

Formula 3

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

Problems connected Rhombus with Detailed Solutions

Problem 1

The size of the purblind angle of a rhombus is twice the size up of its pointed angle. The side duration of the rhombus is adequate 10 feet. Find the area of the rhombus. Solution to Trouble 1:

• A rhomb has 2 congruent different acute angles and ii superposable opposite obtuse angles. One of the properties of a rhombus is that whatever two inward consecutive angles are supplementary. Let x be the acute slant. The obtuse angle is twice: 2x. Which gives the following equation.
  x + 2 x = 180 degrees.
  
• Wor the above equivalence for x.
  3x = 180 degrees.
  x = 60 degrees.
  
• We use formula 2 for the area of a rhombus knowing the side length and one of the angles.
  area of rhombus = (10 feet) ² sin (60 degrees)
  = 86.6 feet ² (rodlike to 1 decimal place)

Problem 2

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

Problem 3

The circumference of a rhomb is 120 feet and unity of its diagonal has a duration of 40 feet. Find the area of the rhombus. Solution to Problem 3:

Many References and Links to Geometry

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

a square is a rhombus with all angles congruent

Source: https://www.analyzemath.com/Geometry/rhombus_problems.html

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