Rhombus and Trapezoid are two of the most commonly studied shapes in geometry. The two shapes may look similar, but they differ in a lot of ways. To help you better understand Rhombus and Trapezoid, let’s compare these two shapes.

Rhombus

A Rhombus is a parallelogram with four equal sides. It is a type of quadrilateral, which means it has four sides, four angles, and four vertices. The opposite sides of a rhombus are parallel, and the adjacent sides are at right angles to each other.

Rhombus is also known as a diamond, and it gets its name from the Greek word “rhombos,” which means “spin top.” The reason why it’s called a diamond is the shape, which is similar to the shape of a diamond.

Trapezoid

A Trapezoid is a quadrilateral with exactly one pair of parallel sides. A trapezoid can be a right trapezoid, an isosceles trapezoid, or a general trapezoid.

The base of a trapezoid is one of the parallel sides, and the other side is called the top side, or the shorter leg. The legs of a trapezoid are the two sides that are not parallel. The height of a trapezoid is the perpendicular distance between the top and base sides.

Comparison between Rhombus and Trapezoid

Symmetry

In terms of symmetry, Rhombus has two lines of symmetry, while Trapezoid has none. Rhombus can be folded in half vertically and horizontally, creating two lines of symmetry. Trapezoid, on the other hand, cannot be folded to create any lines of symmetry.

Angles

Rhombus has four equal angles that are all 90 degrees. Trapezoid, on the other hand, has two acute angles and two obtuse angles. The acute angles are opposite each other, as are the obtuse angles.

Sides

Rhombus has four equal sides, while Trapezoid has two parallel sides and two non-parallel sides. The parallel sides of Trapezoid are usually referred to as the base and the top. The lengths of the two non-parallel sides can be different or equal.

Diagonals

The diagonals of a Rhombus bisect each other at right angles. Each diagonal of a Rhombus is also perpendicular to the other diagonal. It’s worth noting that the diagonals of Rhombus are not equal in length, except in the case of a square, which is a special type of Rhombus.

The diagonals of a Trapezoid, on the other hand, do not bisect each other at right angles. They may or may not be equal in length, depending on the type of trapezoid.

Area

The area of a Rhombus is equal to half the product of its diagonals. A formula to find the area of Rhombus is:

Area = (d1 x d2) / 2

Where d1 and d2 are the lengths of the diagonals.

The area of a Trapezoid can be found using the formula:

Area = ((b1 + b2) / 2) x h

Where b1 and b2 are the lengths of the two parallel sides, and h is the height of the Trapezoid.

Frequently Asked Questions (FAQs)

Q: Can all Rhombuses be considered as a Parallelogram?

A: Yes, all Rhombuses can be considered as a Parallelogram, but not all Parallelograms can be considered as a Rhombus. In a Rhombus, all four sides are equal, but in a Parallelogram, only opposite sides are equal.

Q: What is the difference between a Trapezoid and a Parallelogram?

A: A Trapezoid has only one pair of parallel sides, while a Parallelogram has two pairs of parallel sides. The opposite sides of a Parallelogram are equal in length, while the sides of a Trapezoid may or may not be equal in length.

Q: What is the difference between a Rhombus and a Square?

A: A Square is a special type of Rhombus, where all four sides are equal in length, and all four angles are right angles. Rhombus, on the other hand, has four equal sides, but its angles may or may not be right angles.

Q: Is a Trapezoid a regular polygon?

A: No, a Trapezoid is not a regular polygon because it has no symmetry.

Q: How can I tell if a shape is a Trapezoid?

A: A Trapezoid is a quadrilateral with exactly one pair of parallel sides. If a shape has one pair of parallel sides, it is a Trapezoid.