A parallelogram is a quadrilateral that consists of two pairs of sides that are mutually parallel to each other and are equal in length. The area of a parallelogram can be obtained by calculating the product of its base and height, where the base is one of the parallel sides and height corresponds to the altitude drawn from one corner to the base of the polygon. The perimeter i.e., the length of the outer boundary of a parallelogram is twice the sum of the length of its adjacent sides. In simple words, a parallelogram is a rectangle that is stretched by holding its opposite corners.
Properties of Parallelogram
1. The opposite sides of a parallelogram are parallel and equal in length.
2. The opposite angles of a parallelogram are congruent.
3. The sum of the adjacent angles of a parallelogram is equal to 180°. Hence, the consecutive angles of a parallelogram are supplementary.
4. If any one of the angles of a parallelogram is a right angle, then the rest of the angles will be 90° each. In such a case, the resultant geometric figure is known as a rectangle.
5. The diagonals of a parallelogram bisect each other.
6. The two triangles formed by joining the opposite corners of a parallelogram are congruent to each other.
7. The sum of the square of all the sides of a parallelogram is equal to the sum of the square of its diagonals. This relation is known as the parallelogram law.
Examples of Parallelogram
Tiles come in a variety of shapes and sizes. The most popular shapes used by the industries to manufacture wall and floor tiles are rectangle, square, rhombus, and parallelogram. Hence, tiles constitute a perfect example of parallelogram-shaped objects used in everyday life.
In the modern world, a number of geometric figures are being used by architects to construct unique design buildings. One of the most popular geometric shapes used by builders in the fabrication of buildings is a parallelogram. For instance, the dockland office building located in Hamburg, Germany is parallelogram-shaped.
If you observe the side look of a gable roof, saltbox roof, or shed roof of a house, you can easily visualize a two-dimensional geometric plane quadrilateral that consists of two pairs of parallel and equal sides. Hence, the roofs are a prominent example of parallelogram-shaped objects present around us.
Craft papers that are used to make artefacts are available in a variety of shapes and sizes. One of the most common shapes in which the craft papers are available is a parallelogram. Hence, it is yet another example of parallelogram-shaped objects present around us.
Desks or tables are usually rectangular or square in shape. A rectangular table consists of two pair of parallel sides that are equal in length. Hence, a rectangular is also a parallelogram. This is the reason why rectangular tables are also a prominent example of parallelogram-shaped objects used in daily life.
A number of stationery items and school supplies are available in the shape of a parallelogram. For instance, most of the erasers that we use in daily life are parallelogram-shaped.
7. Solar Panels
Solar panels are usually manufactured in two popular geometric shapes, namely a rectangle and a parallelogram. The parallelogram-shaped solar pannels are usually preferred because it is easy to attach them to the sides of the shed roofs of houses. Hence, solar panels are a prominent example of parallelogram-shaped objects used in daily life.
8. Striped Pole
A pole painted with broad slanting coloured stripes forms a perfect example of a parallelogram. If you carefully observe the boundary lines of the inclined stripe painted on the pole, it forms a quadrilateral that closely resembles a stretched rectangle. Hence, it is yet another example of a parallelogram shape seen in everyday life.
9. Steps of a Stair Case
If you carefully look at the shape of the steps of a staircase, you can easily visualize a parallelogram. Hence, the steps of a staircase form a prominent example of parallelogram-shaped objects present around us.
10. Design on a Cardigan
The design formed on cardigans and sweaters is generally a fancy amalgamation of different geometric figures. One of the popular geometric figure used by the hosiery and knitting industries to design woollen clothes is a parallelogram.
11. Structure on the Fret Board of a Guitar
If you look at the fretboard of a guitar you will find certain marker dots present on the frets number 3, 5, 7, 9, 12, 15, 17, 19, 21, and 24. Sometimes the marker dots are replaced by the bars. These bars are generally shaped like a parallelogram. Hence, the parallelogram shape can be easily located in real life by looking at the marker bars present on the fretboard of a guitar.