Rhombus and Trapezoid: Understanding Two of the Most Common Geometric Shapes

Geometry is the branch of mathematics that focuses on the study of shapes, structure, size, and their relative position in space. Notably, there are various types of geometric shapes which include circles, triangles, squares, rectangles, rhombuses, trapezoids, etc. In this article, we’ll take a closer look at two of these shapes- the rhombus and trapezoid. We’ll define each shape, their properties, and discuss some real-life applications of these common shapes.

What is a Rhombus?

A rhombus is a type of parallelogram whose adjacent sides are equal in length. It is a quadrilateral that has two pairs of parallel sides, and each vertex is formed by the intersection of adjacent diagonals. A rhombus has the following properties:

• All four sides of a rhombus are equal in length.

• The opposite angles in a rhombus are congruent. This means that the adjacent angles add up to 180⁰.

• The diagonals of a rhombus bisect each other.

• The area of a rhombus can be calculated using the formula A = ½ (d1 * d2) where d1 and d2 are the lengths of the diagonals.

Real-life application of Rhombus

Rhombuses have several applications in real life, some of which include:

• Diamond rings- The rhombus is used in designing diamond rings, earrings, and other precious stones.

• Traffic signs- Some traffic signs (No entry, warning signs) are rhombus-shaped.

• Logo designs- Many logos designed by different organizations around the world (e.g. FedEx, Mitsubishi Electric, etc.) incorporate rhombus shapes.

• Window panes- Some window panes have a rhombus shape which makes them seem like diamonds.

What is Trapezoid?

A trapezoid is a quadrilateral that has one pair of parallel sides. It looks like an irregular or flattened rectangle, with one pair of opposite sides being parallel to each other. A trapezoid has the following properties:

• The parallel sides of a trapezoid are called bases. The perpendicular distance between the bases is called the height of the trapezoid.

• The non-parallel sides of a trapezoid are also called legs. Although the legs are of different lengths, the opposite legs are equal in length.

• The sum of the angles in a trapezoid equals to 360°, just like any other polygon.

• The area of a trapezoid can be calculated using the formula A = ½ (b1 + b2) × h, where b1 and b2 are the lengths of the bases, and h is the height.

Real-life application of Trapezoid

Trapezoids have several applications in real life, some of which include:

• Floor plans- Architects use trapezoids in designing floor plans of houses, office buildings, and other structures.

• Roof designs- Trapezoids are also used in designing roof shapes.

• Billboards- Some billboards are shaped like trapezoids, making them more visible for those traveling on the road.

• Table tops- Some table tops have a trapezoid shape instead of rectangular or square-shaped tops, giving them a unique look.

Conclusion

In conclusion, geometric shapes may seem simple, but they are essential in our daily lives. Understanding these shapes and their properties helps us appreciate the significance they play in our environment. The rhombus and trapezoid, as discussed in this article, are just two of the many geometric shapes that exist. By knowing their properties and applications, we can appreciate their use in our daily lives. Next time you see a diamond ring, billboard, logo, or window pane, remember that these things are made possible by geometric shapes like the rhombus and trapezoid.