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What is Perimeter?
In geometry, perimeter can be defined as the path or the boundary that surrounds a shape. It can also be defined as the length of the outline of a shape.
The word perimeter has been derived from the Greek word ‘peri’ meaning around, and ‘metron’ which means measure. Perimeter is the total length of the sides of a 2-dimensional shape. We often find the perimeter when putting up Christmas lights around the house or fencing the backyard garden. Other examples may include finding the total length of the boundary of the soccer field or the length of the crochet or ribbon required to cover the border of a table mat.
How to find perimeter?
We use a ruler to measure length of the sides of a small regular shape. The perimeter is determined by adding the lengths of the sides/edges of the shape. For small irregular shapes, we can use a string of thread and place it exactly along the boundary of the shape, once. The total length of the string used along the boundary is the perimeter of the shape.
| Polygon Name | Perimeter Formula |
|---|---|
| Equilateral Triangle | P = 3 x a |
| Scalene Triangle | P = a + b + c |
| Square | P = 4 x a |
| Rectangle | P = 2 ( a + b ) |
| Quadrilateral | P = a + b + c + d |
| Regular Pentagon | P = 5 x a |
| Regular Hexagon | P = 6 x a |
| Regular Octagon | P = 8 x a |
| Regular N-gon with each side a units long | P = n x a , where n is the number of sides and a is the length of the sides. |
The perimeter of all polygons can be determined by adding the lengths of their sides/edges.
Fun Facts The Perimeter of a circle is called the circumference. Circumference is calculated using the formula 2π × r .
What is Area?
In geometry, the area can be defined as the space occupied by a flat shape or the surface of an object. The area of a figure is the number of unit squares that cover the surface of a closed figure. Area is measured in square units such as square centimeters, square feet, square inches, etc. The origin of the word area is from ‘area’ in Latin, meaning a vacant piece of level ground. The origin further led to an irregular derivation of area as ‘a particular amount of space contained within a set of boundaries’.
We often find the area of the room floor to determine the size of the carpet to be bought. Covering the floor with tiles, covering the wall with paint or wallpaper or building a swimming pool are other examples, where in the area is computed.
Common simple shapes and polygons have their own formulae for calculating area.
| Name of Shape | Area Formula |
|---|---|
| Circle | πr², where r is the radius. |
| Triangle | 1/2 bh, where b is base and h is height. |
| Square | l × l, where l is the length of each side. |
| Rectangle | l × w, where l is length and w is width. |
| Parallelogram | b × h, where b is base, and h is perpendicular height. |
| Trapezium | 1/2 (a +b)h, where a and b are lengths of the parallel sides, and h is perpendicular height. |
In real life, not every plane figure can be clearly classified as a rectangle, square or a triangle. To find the area of a composite figure which consists of more than one shape, we need to find the sum of the area of both or all the shapes forming the composite figure.
The area of the outside surface of a solid or 3-dimensional shape is called Surface Area. For instance, a rectangular prism has 6 rectangular bases and lateral faces. So, the total surface area is the sum of the areas of all the 6 rectangles.
Fun Facts Among all the shapes with same perimeter, a circle has the largest area.
Reference
https://www.splashlearn.com/math-vocabulary/geometry/perimeter