Perimeter Formulas

Perimeter Formulas

A perimeter is the length of a two-dimensional shape’s boundary. It is sometimes described as the total length of the object’s sides. The perimeter of that shape is equal to the algebraic sum of the lengths of its sides. For the various geometric shapes, there are different Perimeter Formulas. The path or boundary that surrounds a shape is known as its perimeter. Students come across a variety of shapes in geometry, ranging from 2D to 3D ones. The formulas of many 2-D geometric shapes are covered by Perimeter Formulas. Students should study the various Perimeter Formulas for different shapes and work through a few examples. There are numerous uses in real life for perimeter calculations. A calculated perimeter is the length of fencing needed to completely encircle a yard or garden. The circumference of a wheel or circle, which measures its perimeter, indicates how far it may travel in a single rotation. Similar to this, the perimeter of a spool is related to the length of the string looped around it; if the string’s length were correct, it would match the perimeter. In geometry, the term perimeter is first presented to students. The whole length of a closed shape’s boundary is the shape’s perimeter. The shape could be made up of curves or segments of straight lines. Polygons are shapes composed of line segments. One can get the perimeter of a polygon by combining the lengths of all of its line segments.  Perimeter is a unit of measurement that has only one dimension and can be expressed in feet, yards, millimetres, metres, or miles.  For instance, if one wants to fence a plot of agricultural land with barbed wire, then they may determine the length of wire needed by determining the area’s perimeter.

Meaning of Perimeter Formulas

The distance around the two-dimensional shape is calculated using Perimeter Formulas by summing the lengths of its sides. The whole length of a shape’s sides is referred to as its perimeter. Students can determine the Perimeter Formulas if they are aware of the shape’s measurements. The Perimeter Formulas for each polygon varies based on the geometry of the object. Polygons are important in finding perimeters not only because they are the simplest shapes, but also because the perimeters of many shapes are approximated by sequences of polygons tending to these shapes. The first known mathematician to have used this line of thinking was Archimedes, who calculated a circle’s approximate perimeter by enclosing it in a regular polygonal pattern. Geometrical Perimeter Formulas for various shapes are given by the Extramarks platform for help. In Mathematics, perimeter is frequently used for word problems in geometry and calculus optimization problems. In real life, perimeter has a wide range of uses beyond just determining an object’s surface area. Perimeter has several uses in the fields of business, housing, building, gardening, and crafts. For instance, a gardener might use perimeter to determine the appropriate length of fence to enclose a rectangular garden. In order to determine how much paint to purchase for a project, a painter considers the perimeter. In fact, there are many more real-world uses for perimeters, including building construction and area optimization.

Perimeter Formula of Different Shapes

A closed path that covers, encircles, or outlines a one-dimensional length or a two-dimensional shape is called the perimeter. A circle’s or an ellipse’s circumference is referred to as its perimeter. The total length of all the sides of any geometric shape can be calculated using the Perimeter Formulas. Depending on the shape and size, many geometric shapes have a formula for the perimeter. Students should study the Perimeter Formulas for these shapes thoroughly. An equilateral polygon is one that has all of its sides the same length (for example, a rhombus is a 4-sided equilateral polygon). An equilateral polygon’s perimeter can be calculated by multiplying its number of sides with the average length of its sides. The number of sides and circumradius, or the constant distance between the centre and each vertex, of a regular polygon can both be used to describe it. Its sides’ lengths can be determined using trigonometry. If n is the number of sides and R is the radius of a regular polygon, then its perimeter can be calculated using the Perimeter Formulas.

Perimeter Formula of a Square

The perimeter of a shape is, as students are already aware, its length across its sides, border, or path. By summing the lengths of each side, one may get a square’s perimeter. Students can use the Perimeter Formulas for calculating a square’s perimeter.

Perimeter Formula of a Rectangle

A rectangle is a closed, four-sided geometric shape. Each interior angle of this shape’s opposite sides is a right angle, and its opposite sides are congruent and parallel. A rectangle’s perimeter is equal to twice the sum of its length and width. The distance that the boundary or all four sides of a rectangle cover determines a rectangle’s perimeter. A rectangle’s perimeter is equal to twice the sum of its length and breadth. Therefore, the Perimeter Formulas for a rectangle’s perimeter can be calculated using its length and breadth. 

Perimeter Formula of a Triangle

A closed geometric shape with only three sides is a triangle. The lengths of all three sides add up to get the triangle’s perimeter. By summing all the sides—in this case, all three sides—of a triangle, one can determine the Perimeter Formulas. For various kinds of triangles, various Perimeter Formulas are applied. But the general formula for calculating a triangle’s perimeter can be also used. Sum of the three sides equals the perimeter of a triangle. There are different Perimeter Formulas for several kinds of triangles. A scalene triangle’s perimeter is equal to the sum of its three distinct sides. The perimeter of an isosceles triangle is equal to the sum of one side and twice the length of the other two equal sides. An equilateral triangle’s perimeter is equal to three times the length of each side.

Perimeter Formula of a Parallelogram

A parallelogram is a closed, four-sided geometric shape. In a parallelogram, the opposing sides are parallel and congruent. The sum of all the sides that are equal to one another yields the formula for a parallelogram’s perimeter. However, if the sides of the object are omitted but the diagonals or an angle remain, the Perimeter Formulas for a parallelogram can also be derived. As a result, the Perimeter Formulas can be used to determine a parallelogram’s perimeter.

Perimeter Formula of a Circle

A circle is a closed curve that may be drawn by drawing a line that is fixedly spaced from a fixed point in geometry. In contrast to polygons, a circle lacks vertices and edges. The circumference of a circle is equal to twice the radius times pi, and it is expressed as a number. A circle’s perimeter formula is made up of two primary components: two constants and one radius of the circle. The circumference of a circle is the formula for a circle’s perimeter.

Perimeter Formula of a Rhombus

Both a square and a rhombus are closed four-sided geometric forms. Each internal angle of a square is a right angle, but not so with a rhombus. Both of these quadrilaterals have perimeters that are four times their side lengths. The lengths of all the sides of a rhombus are added to determine the Perimeter Formulas. The formula for calculating the perimeter of a rhombus can be determined under two conditions: when the sides are known and when the angles are known. So, the formula for a rhombus’s perimeter is four times the length of the sides.

Perimeter Formula of a Trapezoid

Like squares, parallelograms, and rectangles, a trapezoid is a closed four-sided geometric shape. There is just one pair of opposing sides that are parallel to one another in this shape. The total length of all the sides makes up a trapezoid’s perimeter. The lengths of all four sides of a trapezoid are added to determine the perimeter of the shape. A trapezoid’s Perimeter Formulas ensures that the entire boundary is included. Thus, the following formula can be used to determine a trapezoid’s perimeter:

A trapezoid’s perimeter, P, is equal to the sum of all of its sides, which are denoted by the letters a, b, c, and d, respectively.

Perimeter Formula of a Kite

The kite is a closed geometric object with four sides that has equal lengths on both pairs of adjacent sides. A kite’s perimeter is equal to twice the length of two of its unequal sides added together. A kite’s perimeter is measured by adding all of its sides, and its distance is determined by adding the sides of each pair. Thus, the following formula can be used to determine a kite’s perimeter. P = 2(a+b), where a and b are the lengths of the two pairs of kites, is the formula for a kite’s perimeter.

Perimeter Formula of Polygons

Due to the fact that polygons are closed plane shapes, their perimeters likewise reside in a two-dimensional plane. By determining the polygon’s total length, the Perimeter Formulas can be determined. There are two methods for calculating the perimeter of polygons: in relation to regular and irregular polygons. The formula can be used to determine a regular polygon’s perimeter. For regular polygons, perimeter equals length multiplied by the number of sides. For irregular polygons, the sum of all sides equals the irregular polygon’s perimeter.

Examples Using Perimeter Formula

Examples on the Perimeter Formulas are provided by the extramarks platform for more practice on this concept.