Formula for Perimeter of Geometrical Shapes

Geometry is a discipline of mathematics that analyses the dimensions, sizes, forms, and angles of objects. 2D forms are flat geometric shapes such as squares, circles, and triangles. The length and width of these forms are the only dimensions. Geometry can be divided into the following parts:

1. Plane Geometry: Platforms that can be drawn on paper are the focus of plane geometry. In two dimensions, lines, circles, and triangles are examples. Two-dimensional geometry is sometimes known as plane geometry. There are only two dimensions in all two-dimensional figures: length and width. The depth of the shapes is not taken into account. Squares, triangles, rectangles, circles, and other plane figures can be found.

2. Solid Geometry: Three-dimensional structures such as cubes, prisms, cylinders, and spheres are studied in solid geometry. It is concerned with the three dimensions of the figure, namely length, width, and height. Certain solids, on the other hand, do not have faces (e.g. sphere). Solid geometry refers to the study of three dimensions in Euclidean space. Our surroundings have three-dimensional structures. Rotating two-dimensional shapes produces both three-dimensional shapes. Faces, corners, and vertices are all important features of 3D shapes.

What is the Perimeter formula?

The perimeter of a two-dimensional shape is the length of its boundary. It’s also known as the total of all the object’s sides. The perimeter of a shape is equal to the algebraic sum of each side’s length. For the numerous shapes in geometry, we have formulas available.

Shape	Perimeter Formula
Circle	2πr
Triangle	p + q + r, where p, q, and r are the sides of the triangle
Square	4m, where m is the length of the side of the square
Rectangle	2(L + B), where L is length and B is the breadth
Trapezium	p + q + r + s, where p, q, r, and s are the sides
Isosceles Right Triangle	2x + y, where x is the sides and y is the hypotenuse
Rhombus	4m, where m is the length of the side of the rhombus
Equilateral Triangle	3m, where m is the length of the side of an equilateral triangle
Any Polygon	2mR sin (180°/m), where m represents the number of sides and R represents the circumradius (means the distance from the center to one of the vertices of the polygon)
Parallelogram	2(am + bm), where am and bm are adjacent sides

How to find perimeter?

Perimeter is a term that refers to the area that surrounds an object. Apart from the formulas mentioned above, there are other methods for determining the perimeter of a given shape. A ruler can be used to measure the length of the sides of a tiny regular shape, such as a square, rectangle, parallelogram, or other similar shapes. By summing the measurements of the shape’s sides and edges, the perimeter will be calculated.

For little irregular shapes, we can use a string or a thread. Place a string or thread along the figure’s edge once in this situation. The perimeter of a form is the total length of the string used along its edge.

Units of perimeter

When representing the parameters of any geometric figure, units are required. For example, the length of a line segment can be measured in cm or m, where cm and m are the length measurement units. Perimeter is measured in the same units as the length of the sides or a specific parameter. When the length of a square’s side is specified in centimeters, the perimeter units are also given in centimeters. Another situation is when the dimensions are supplied in two different units, such as the length of a rectangle in ft and the width in inches; in this case, the perimeter of a rectangle will be measured in ft, and both measures must be converted to ft.

Difference between area and perimeter

The perimeter is the total distance traveled around the edge of the shape, whereas the area is the space occupied by the shape. The area of a flat surface of a specific shape is defined as the amount of space it covers. It is calculated as a “number of” square units (square yards, square inches, square feet, etc.). The edges and corners of most objects and forms are present. When computing the area of a shape, the length and breadth of these edges are taken into account. The perimeter, on the other hand, is the measurement of length covered by the shape’s boundary.

Sample Questions

Question 1: What is the perimeter of an equilateral triangle given side length is 7 cm?

Solution:

The side length of an equilateral triangle is 7 cm.

The equilateral triangle, as we all know, has all of its sides of equal length.

Therefore,

Triangle perimeter = p + q + r

Here,

p = q = r 

Therefore, the perimeter of  equilateral triangle = 3a

So,  P = 3 x 7 = 21 cm

Question 2: If the radius of a circle is 21 cm, then find its perimeter.

Solution:

Given,

Radius of circle = 21 cm

As we know that perimeter of circle = Circumference of circle = 2πr

Therefore,

Circumference = 2 × 22/7 × 21

= 2 × 22 × 3

= 132 cm

Therefore, the perimeter of circle here is equal to 132 cm.

Question 3: A regular pentagon of side 3 cm is given. Find its perimeter.

Solution:

According to the question

Length of the side of pentagon = 3 cm

As we already know that a regular pentagon 5 sides and they are equal in length 

Hence,

The perimeter of regular pentagon = 5a, where a is the side length

Perimeter = 5 × 3

= 15 cm

Therefore, the perimeter is 15 cm.

Question 4: If the length of a rectangular-shaped notebook is 9 units and the width is 5 units, what is the perimeter?

Solution:

The length and breadth parameters are as follows: length = 9 units and breadth = 5 units.

Using the formula 2(length + breadth) to calculate the perimeter of a rectangle

Notebook perimeter = 2(9 + 5) = 28 units

As a result, a notebook’s perimeter is 28 units.

Question 5: A chocolate bar is made up of equal-sized squares, each measuring 2 inches on each side. Calculate the perimeter of the object.

Solution:

As we know that all of the sides of each small square are equal to one inch. 

So, we get 6 inches if we count and add the sides of squares along with length. Along the length of the bar, the sides of squares add up to 4 in. 

As a result, the bar’s length is 6 in. The bar’s width is 4 inches.

So the perimeter = 2(6 + 4) = 20

The chocolate bar’s circumference is 20 inches.