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The perimeter of a shape is the comprehensive measurement of all its edges. All the shapes begin with a line or a line segment furthermore it can also begin with a curve. The number and the arrangement of these lines are used for deciding the type of shape. Every shape has a different interior region or a surface that is bounded by these lines. All these bounded lines help in the perimeter of all the geometric shapes and also the formula for each of the shapes. They may vary from one shape to the other one. A square lot of shapes in our day-to-day life like rectangles, triangles, circles, or a square. All the shapes have different perimeters. Here, we will be learning more about the perimeter of shapes and discussing some important questions.
Read Also: Congruence of Triangles
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Keywords: What is the Perimeter, the perimeter of shapes, the perimeter of different Shapes Formula, Rectangle, Square, Circle, Triangle.
What is the Perimeter?
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The perimeter can be defined as the path that helps in circumscribing a two-dimensional shape. It is also used in one-dimensional shapes. The word Perimeter is derived from conjoining two Greek words Peri & Metron where Peri means around & Metron means Measure. The perimeter can be illustrated as the length of its outline. A has length & breadth but it has no depth. It can be measured in centimeters or meters. When we add the total of all the edges of a shape we got the perimeter of that shape.
The Perimeter of Shapes
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The perimeter of a shape is the measurement around the edges of shapes. It is the distance around a two-dimensional shape. The path or boundary that surrounds a shape is called its perimeter. Furthermore, it can also be defined as the length of the outline of a shape. Every shape has a different perimeter according to its length, width & depth. But there is one formula that remains the same for every shape.
The Perimeter of Shapes
Perimeter formula of Different shapes:
The Formula:
Perimeter formula of Shapes = Total Length of the Boundary of shapes
Also check: Area of shapes
The Perimeter of Different Shapes Formula
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The formula for the perimeter of different geometric shapes varies from one shape to the other one. Here we are listing some common shapes with their perimeter formulas:
The Perimeter of a Square
A square is also a polygon because it has four sides & all the sides of a square are equal. A square or a polygon has four angles of equal size.
The perimeter formula
Perimeter formula of a Square = Sum of all the four sides
Square
So as per the above image, it can be calculated as;
= a + a + a + a
= 4a
The perimeter formula of a square = 4 × side
Read More: Area of a Square
The Perimeter of a Rectangle
A rectangle is a shape with four sides. It can also be called a four-sided polygon that has two dimensions length & breadth.
The Perimeter Formula
The perimeter formula of a rectangle = The sum of Four sides
Rectangle
According to the above image, it can be calculated as;
= AB + BC + CD +AD
= length (L) + breadth (B) + length (L) + breadth (B)
= 2 lengths + 2 breadth
The perimeter of rectangle= 2 × (length +breadth)
The Perimeter of a Circle
A circle can be defined as a collection of points. The perimeter of a circle is called the circumference of a circle which is equal to 2πr.
r is the radius which is the distance from the center to any point on the edge of the circle.
Circle
The perimeter formula.
The perimeter of a circle= 2πr = πd
r = the radius which is the distance from the center towards any point on the edge of the circle
d = diameter of the circle
π (pi) = approx measures at 3.42
Also Read: Perimeter and Area of a Circle
The Perimeter of a Rhombus
A Rhombus is a way similar to a polygon. It has four sides & four angles. All the sides of a rhombus are not 90°. A rhombus looks like a diamond. It can also, be called That it is a diamond-shaped object.
The Perimeter Formula
Perimeter formula of a rhombus (P) = 4 × S
S = length of the side.
Rhombus
The Perimeter of a Triangle
A triangle can be defined as a three-sided polygon with three vertices. It has three sides & it can be equal in size or can unequal consequently.
The perimeter Formula
The perimeter of a triangle = total of all the sides
= a + b + c
The perimeter
Triangle
Check Also: Area of a triangle
The Perimeter of a Quadrilateral
A flat shape that has parallel sides & these sides are equal in length is called a Quadrilateral. These parallel sides are opposite to each other.
The Perimeter Formula
The perimeter of A Quadrilateral = Total of the sides
Perimeter formula = a + b + c + d
Quadrilateral
The Perimeter of a Parallelogram
A parallelogram is also a quadrilateral but it is it a little different from it? It has both pairs of opposite sides that are parallel to each other.
The Perimeter Formula
The Perimeter of a Parallelogram (P) = 2 (PQ + PS)
Parallelogram
Check Important Difference between Area and Perimeter
The Perimeter Formula of a Kite
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We all know the shape of a kite. It has a shape similar to a rhombus. It is calculated by adding all the sides & distance is calculated by adding the sides of each of the pairs.
The perimeter Formula
The perimeter of a kite (P) = 2 (a + b)
A & b are the lengths of the two pairs.
Kite
Check More: Perimeter of Kite and its Formula
The Perimeter of a Polygon
A polygon can be of two types it can be regular or irregular. It is a two-dimensional closed plane shape. The perimeter of a polygon can be calculated by measuring the sum of the length of the polygon.
The perimeter formula
Regular polygon
- Perimeter of Hexagon = 6 × (length of one side)
- Perimeter of Pentagon = 5 × (length of one side)
Irregular polygon
The perimeter of irregular polygon = the sum of all sides.
Irregular polygon
Read More: Mensuration formula
Things to Remember
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- All the regular shapes have all the sides of equal lengths & that’s why it is easy to find out the perimeter of a regular shape.
- If we need to find out the side length of a regular shape then we can find it using the perimeter of the shape, we just need to do is to divide the perimeter with the number of sides & we will get the side length of that particular shape.
- When two or more rectangles are connected then they result in making the rectilinear shape.
- The perimeter of a circle is more popular than the circumference of the circle as it is the length of the boundary of the circle.
- A circle has the largest area among all the two-dimensional shapes & still, the area has the same perimeter.
Sample Questions
Ques: Find out the perimeter of a square with a side of 7 cm? (3 marks)
Ans: As given,
Length of the side of a square = 7 cm
The perimeter formula of a square= 4a
= 4 × 7 cm
= 28 cm
Hence, the perimeter of a square is 28 cm.
Ques: Determine the length of the side of the equilateral triangle, if the perimeter of the triangle is 15 units. (3 marks)
Ans: As given,
Perimeter of Equilateral triangle = 15 units
Let’s assume that the side of the triangle is = a
The perimeter Formula
P= 3× a
15= 3× a
A= 15/3
A= 5 units
Thus, the length of the side of the equilateral triangle is 5 units.
Ques: If the perimeter of a square is 35 units then find out the side of the square? (3 marks)
Ans: As Given,
The perimeter of a Square
P= 35 units
The perimeter formula :
P= 4 × side units
35 = 4 × Side
Side= 35/4
Side= 8.75 units
Hence, the side of the square is 8.75 units.
Ques: if the perimeter of a square is given 45 units then find out the side length? (3 marks)
Ans: As given,
The perimeter of square P= 45 units
The perimeter formula
P= 4 × side units
45= 4 × side
Side= 45/4
Side= 11.25 units,
Therefore, the Side of the square is 11.25 units.
Ques: Which shape has the largest area? (3 marks)
Ans: Among all the two-dimensional shows the circle has the largest area. It has the largest area and the same perimeter. A circle is equal in length with all the sides because it has a round shape. Moreover, A cyclic polygon also has a large area but as it has been charged in a circle. But still, it can be said that it has the ten largest are among all the polygons. A cyclic polygon has a provided number of sides & all these sides have the same length.
Ques: Find out the perimeter of a square if the side length of the square is given 14 cm. (3 marks)
Ans: As given,
The length of the side = 14 cm
perimeter formula of a square= 4a
= 4 × 14
= 56 cm
Hence, The perimeter of the square is 56 cm.
Ques: How can we find the perimeter of regular shapes? (4 marks)
Ans: A regular shape is a two-dimensional shape like rectangle, square, triangle & circle, .c. The sides of .regular shape are equal whether it has four sides or three the length of all the sides is equal. The sum of all the sides of a regular shape is the perimeter of that particular shape. For finding out the perimeter of a shape we need to measure all its sides first. The second thing we need to do is multiply the number of the sides by ten lengths on each side. After flowing this process we will get the perimeter of a regular shape.
Ques: What are the perimeters and the areas? (4 marks)
Ans: Perimeters & the area are some of the most essential topics in Mathematics. With the help of these two, we can easily measure the physical space. The perimeters & area also contribute towards a more advanced mathematics base that is found in different branches of mathematics like, Trigonometry, Algebra & Calculus, etc.
The perimeter of a shape is the total boundary of a two-dimensional shape it is measured in Centimeter cm or in meters m. On the other side, the area refers to the total surface that a shape covers & it is measured in square units.
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