How to Calculate the Perimeter of Common Shapes
What is Perimeter?
In geometry, the term Perimeter refers to the path that circumscribes a two-dimensional shape. However, in one-dimension, it can either be used for the path or its length. The word perimeter has its roots in Greek and has been framed by conjoining two Greek words peri (around) and metron (measure). Perimeter is the length of an outline of a shape; calculation of a distance around something or some object. The Perimeter is measured in either centimetre (cm) or meter (m).
A two–dimensional figure points to any shape which lies on a surface and has length and breadth but has no depth. Similarly, one-dimensional figures refer to lines that lie in one plane.
Each polygon is a two-dimensional figure which lies on a flat surface. Polygons are plane shapes two dimensional that have straight sides. In mathematics, each figure or mathematical model is obtained from objects in real-world that have similar geometric properties.
The Perimeter of Different Shapes Formulas
With changing shape, formulas of mathematical figures also vary. To help students understand the Perimeter of different shapes formulas more broadly, a list is provided below that answers the question of different shapes.
What is the Perimeter of a Rectangle?
In geometry, a rectangle is a two-dimensional shape which has four sides and four corners. The formula to find the perimeter of a rectangle is described below,
Perimeter of a rectangle=sum of all four sides.
Therefore, perimeter of the given rectangle is
=Length + breadth + length + breadth
=7+3+7+3=20
Also, perimeter of a rectangle=2x (length + breadth)=2x10=20
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What is the Perimeter of a Triangle?
A triangle is a three-sided polygon that has three vertices. The process of finding the Perimeter of a triangle is shown below,
Perimeter of a triangle = a+b+c
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What is the Perimeter of a Square?
In geometry, a square is a polygon that has four equal sides and four equal angles. Below is described the formula of finding the Perimeter of a square.
Perimeter of a square= sum of all four sides
=a +a + a + a
=4a
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What is the Perimeter of a Circle?
In geometry, a circle is a shape whose all points lie on the same plane at an equal distance from the centre point. The Perimeter of the circle is known as the circumference. The formula to find out the circumference of a circle is discussed below,
Circumference of a circle =2πxr
Here, r refers to the radius. Radius is the distance from the centre to any point on the circle’s edge.
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What is the Perimeter of Rhombus?
Rhombus is a polygon which has four equal and four angles which are not 90°. It is often called a diamond or diamond-shaped object. The Perimeter of a rhombus is shown below,
Perimeter of a rhombus (P) = 4 X S
Here, S refers to the length of the side of the rhombus.
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What is the Perimeter of Quadrilateral?
In geometry, quadrilateral refers to any flat shape that has parallel opposite sides which are equal in length. The formula of the Perimeter of Quadrilateral is described below,
Perimeter of Quadrilateral= a + b +c + d.
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What is the Perimeter of Parallelogram?
A parallelogram is a quadrilateral that has both pairs of opposite parallel sides. The formula of the Perimeter of described below,
Perimeter of Parallelogram (P)= 2(PQ+ PS)
=2 x (10+6)
=2x16
=32
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FAQs on Perimeter of Shapes Explained for Students
1. What is the perimeter of a shape in simple terms?
The perimeter of a shape is the total distance around its outer boundary. Imagine you are walking along the edges of a polygon, like a park or a field; the total distance you cover to return to your starting point is its perimeter. To calculate it for any polygon, you simply add the lengths of all its sides together. It is measured in linear units like centimetres (cm), metres (m), or inches.
2. What is the main difference between the perimeter and area of a shape?
The primary difference lies in what they measure. Perimeter measures the length of the boundary, while area measures the space enclosed within that boundary. Think of it like a photo frame:
The perimeter is the length of the material needed to make the frame itself.
The area is the size of the photograph that can fit inside the frame.
Because of this, perimeter is measured in linear units (like m) and area is measured in square units (like m²).
3. How do you find the perimeter of common shapes like a rectangle and a square?
You can use specific formulas for regular shapes to find the perimeter quickly:
Perimeter of a Rectangle: Since a rectangle has two pairs of equal-length sides (length 'l' and breadth 'b'), the formula is P = 2 × (l + b).
Perimeter of a Square: A square has four equal sides (side 's'). Therefore, its perimeter formula is P = 4 × s.
4. How is the concept of perimeter used in real-life situations?
Perimeter is a practical concept used in many everyday tasks and professions. Some real-world examples include:
Fencing a garden or yard: To find the total length of fencing required, you need to calculate the perimeter of the area.
Framing a picture or a window: The length of the wooden or metal border needed is determined by the perimeter.
Construction and architecture: To plan the foundation of a building or the layout of a room.
Athletics: To measure the length of a lap on a running track.
5. How is the perimeter of an irregular shape calculated?
For an irregular shape (a polygon where sides are not all equal), there is no special formula. The method is straightforward: you must measure the length of each individual side and then add them all together. For example, if an irregular pentagon has side lengths of 3 cm, 4 cm, 5 cm, 6 cm, and 7 cm, its perimeter would be 3 + 4 + 5 + 6 + 7 = 25 cm.
6. What are the formulas for finding the perimeter of different types of triangles?
The perimeter of any triangle is the sum of its three sides. However, for specific types of triangles, the calculation can be simplified:
Scalene Triangle: Where all three sides (a, b, c) are different lengths, the perimeter is P = a + b + c.
Isosceles Triangle: With two equal sides (a) and a different base (b), the perimeter is P = 2a + b.
Equilateral Triangle: Where all three sides (s) are equal, the perimeter is P = 3 × s.
7. Why is the perimeter of a circle called circumference and how is it calculated?
The perimeter of a circle is called the circumference to distinguish it from the perimeter of polygons, which are made of straight lines. A circle is a continuous curve. You cannot add up its 'sides'. Instead, its perimeter is calculated based on its radius (r) or diameter (d) using a special constant called Pi (π), which is approximately 3.14. The formulas are:
Using radius: C = 2πr
Using diameter: C = πd
8. If two different rectangles have the same perimeter, must they also have the same area?
No, two rectangles with the same perimeter can have very different areas. This is a common point of confusion. For example, a rectangle with sides 9m and 1m has a perimeter of 2(9+1) = 20m and an area of 9 × 1 = 9 m². Another rectangle with sides 6m and 4m also has a perimeter of 2(6+4) = 20m, but its area is 6 × 4 = 24 m². This shows that the shape of the boundary significantly impacts the enclosed area, even if the boundary's total length is the same.
