Rhombus

Definition : A rhombus is a closed two-dimensional shape and it satisfies all properties of a parallelogram. But it has a unique identity due to some special properties. A parallelogram is a quadrilateral in which the opposite sides are parallel. In addition to this condition, all sides of a rhombus are equal and the diagonals of a rhombus intersect each other at 90 degrees. Rhombuses, rhombi, are referred to as diamonds due to their resemblance to the shape of a diamond. A rhombus is also known as an equilateral quadrilateral, as the sides of a rhombus are equal. Rhombuses are also quite similar to squares as both shapes have four equal slides. But a rhombus can look like a slanted square as the four angles of a rhombus need not be 90 degrees at all times. Read More: • All sides of a rhombus are equal and parallel to each other. Rhombus • The opposite angles of a rhombus are equal. • A rhombus cannot be a cyclic quadrilateral, meaning it cannot be inscribed inside a circle, unless it is a square. • The diagonals of a rhombus bisect each other at right angles. • The sum of all interior angles of a rhombus is always 360 degrees. • The sum of the adjacent angles of a rhombus is always 180 degrees (supplementary). • The diagonals of a rhombus bisect its angles. • Perimeter of a rhombus = 4a units, where a is the length of each side. • Area of rhombus \( =\frac \) square units, where \( d_1 \) and \( d_2 \) are its diagonals. • If the length of the shorter diagonal of a rhombu...

How is a Rhombus Different from a Square? The difference between a So, a rhombus with right angles becomes a square. We can say, “ Every square is a rhombus but all rhombus are not squares.” Real-life Examples Rhombus can be found in a variety of things around us, such as finger rings, rhombus-shaped earring, the structure of a window glass pane, etc. Properties of a Rhombus Some of the properties of a rhombus are stated below. • All sides of a rhombus are equal. Here, AB = BC = CD = DA. • • Opposite sides are parallel in a rhombus. Here, AB ∥ CD and AD ∥ BC. • Opposite angles are equal in a rhombus. ∠A = ∠C and ∠B = ∠D. • Adjacent angles add up to 180°. ∠A + ∠B = 180° ∠B + ∠C = 180° ∠C + ∠D = 180° ∠A + ∠D = 180° • All the • Adjacent angles of a rhombus add up to 180°. • The diagonals of a rhombus are perpendicular to each other. Here, AC ⟂ BD. • The diagonals of a rhombus bisect each other. Here, DI = BI and AI = CI. • A rhombus has rotational symmetry of 180 degrees (order 2). That is, a rhombus retains its original orientation when rotated by an angle 180 degrees. • The diagonals of a rhombus are the only 2 lines of symmetry that a rhombus has. These divide the rhombus into 2 identical halves. Area of a Rhombus The area of a rhombus is the region enclosed by the 4 sides of a rhombus. There are two ways to find the area of a rhombus. • Area of a Rhombus When its Base and Altitude are Known Area of rhombus is calculated by finding the product of its base and corresponding...

Paul Mazzola • • • • • Rhombus definition A rhombus is a quadrilateral with four equal-length sides and opposite sides parallel to each other. All rhombuses are parallelograms, but not all parallelograms are rhombuses. The opposite interior angles of rhombuses are congruent and the diagonals of a rhombus always bisect each other at right angles. Tutors What does a rhombus look like? Most times, the rhombus you see will be drawn so it has a base -- two opposite sides will be horizontal, with the bottom side serving as the shape's base. What is a rhombus Be careful, though, because a rhombus can appear at any orientation. When it "stands up" so it is symmetrical in appearance, (its diagonals are horizontal and vertical) it is usually called a diamond. If you struggle to remember its name, think of a square that has been run into by a bus, so it is tilted over ( run into by a bus … rhombus). Is a square a rhombus? All squares are rhombuses, but not all rhombuses are squares. If you have a rhombus with four equal interior angles, you have a square. A square is a special case of a rhombus, because it has four equal-length sides and goes above and beyond that to also have four right angles. Is a rhombus always a parallelogram? A rhombus is a special case of a parallelogram, because it fulfills the requirements of a parallelogram: a quadrilateral with two pairs of parallel sides. It goes above and beyond that to also have four equal-length sides, but it is still a type of paralle...

home / geometry / shape / rhombus Rhombus A rhombus is a Sides of a rhombus All sides of a rhombus are congruent, and its opposite sides are Angles of a rhombus Like a parallelogram, opposite angles of a rhombus are congruent. Also, the adjacent angles of a rhombus are Diagonals of a rhombus A rhombus can have two diagonals; the diagonals are Diagonals AC and BD are perpendicular bisectors of each other for rhombus ABCD above. The diagonals of a rhombus bisect its angles: Diagonals AC and BD Square A Symmetry in a rhombus A rhombus has 2 Line of symmetry Rotational symmetry Both diagonals are lines of symmetry 180° angle of rotation about its center Area of a rhombus The area of a rhombus with diagonals d 1 and d 2 is, Let AC = d 1 and BD = d 2 for rhombus ABCD above. Rhombus ABCD can be divided into triangles ABC and ADC by diagonal AC. The area of △ABC = AC×BE where BE is the altitude of △ABC. The area of △ADC = AC×DE where DE is the altitude of △ADC. The area of rhombus ABCE equals the sum of the areas of △ABC and △ADC. Area = Area of △ABC + △ADC = AC×BE + AC×DE = AC×(BE + DE) = AC×BD = (d 1×d 2) If the length of base (b) and height (h) of a rhombus were given, the area of a rhombus is, A = b·h

Area of Rhombus The area of a rhombus is the amount of space enclosed by a rhombus in a two-dimensional plane. A rhombus is a special type of parallelogram in which all sides are equal to each other. The shape can be differentiated from a square through the measure of its internal angle. The internal angle of a rhombus need not be a right angle specifically. The area of a rhombus can be calculated in different ways, depending on the parameters known to us. Let us learn more about the area of a rhombus, and the area of rhombus formula in this article. 1. 2. 3. 4. What is the Area of a Rhombus? The area of a 2, m 2, in 2, and so on. Rhombus is a • A rhombus is a • The diagonals of a rhombus bisect each other at right angles. • The diagonals of a rhombus are • The area of a rhombus can be found in different ways: using base and height, using diagonals, and using Area of Rhombus Formula The area of rhombus formula depends upon the parameters known to us. There are different formulas based on different parameters as given below: • Formula using Base and height: Area of a Rhombus = base × height • Formula using 1× diagonal 2)/2 • Formula using trigonometry: Area of a Rhombus = side 2 × sin(A) How to Find the Area of a Rhombus? Let us understand the area of rhombus formulas in detail and use them to find the area of a rhombus now. Formula for Area of Rhombus with Base and Height Rhombus is a parallelogram. We know that the area of a parallelogram is calculated by multiplying its ...

A rectangle and a rhombus are both types of parallelograms. However they have different properties of their sides, angles and diagonals. A rectangle has all its angles #90°# A rectangle has two pairs of equal sides - two longer sides and two shorter sides. The diagonals of a rectangle are equal, but do not intersect at #90°# The opposite angles of a rhombus are equal. There are two obtuse angles and two acute angles. All four sides of a rhombus are equal. The diagonals are not equal, but they intersect at #90°# A rectangle is therefore not a rhombus, If it is to be a rhombus, additional properties have to be present. The only time this would happen is if the shape was a square. A square is a rectangle, but a rectangle is not a square.