How To Find The Perimeter Of A Figure With Formula And Solved Examples
The route or boundary that encircles any shape in mathematics is defined by the shape's circumference. To put it another way, the circumference and perimeter both refer to the length of a shape's outline.
What is the Perimeter?
A path that encircles a two-dimensional object is called a perimeter. The word is Greek, peri meaning "around," and "metre" meaning measure. The phrase can refer to either the path or its length; it can be compared to the size of a shape's outline.
How to Find the Perimeter of a Figure?
Steps to find the Perimeter of a given figure:
STEP 1 : Calculate the lengths of the sides.
Usually we don't need a special formula to get perimeter because perimeter is simply a measure of a two-dimensional figure's outline (though there are equations for specific shapes to make it easier).
STEP 2 : The length of each side is added together.
When calculating the perimeter of a non-circular object, add up all of the side lengths to get its perimeter.
STEP 3 : Be careful of the units of measurement.
We need to add all the lengths in the same unit to add else we can't add it (such as feet, miles, or metres).
Perimeter of Square:
Since a square is a polygon with four equal sides, its perimeter will be equal to the sum of those sides.
The formula \[{\rm{P = 4x}}\], where x is the length of one side, can be used to determine whether a square has four equal-length sides.
Square
Perimeter of Rectangle:
The perimeter of a rectangle is determined by adding up all of its sides.
Formula \[ = 2(a + b)\] units
where:
“a” is the length of the rectangle
“b” is the breadth of the rectangle
Rectangle
Perimeter of Circle:
Circumference of the circle or perimeter of the circle is the measurement of the boundary of the circle.
Circle perimeter or circumference is equal to\[2\pi r\] .
where,
r is the circle's radius.
\[\Pi \] is a mathematical constant with an estimated value of 3.14 (to the nearest two decimal places).
Circle
Solved Examples:
1: Find the perimeter of the square whose side is 6 units.
Ans: As we know that all the sides of a square are equal.
And its perimeter is 4 times its side.
Thus, it’s perimeter will be \[4 \times 6 = 24\]
Its perimeter is 24 units.
2: Find the perimeter of the following figure:
Ans: The perimeter of a planar object is the sum of all the sides in it.
It can alternatively be described as the total sum of all of a planar object's bounding sides.
Here,\[AB + BC + CD + DA = 5 + 9 + 7 + 10\] is the total length of all the sides of the provided figure.
Thus, The stated figure's perimeter is 31 metres.
3 :Determine the circle's radius for\[C = 50cm\] .
Ans: Given that 50 cm is the circumference.
According to the formula\[C = 2\pi r\]
This indicates that
\[\begin{array}{l}50 = 2\pi r\\25 = \pi r\\r = 25/\pi \end{array}\]
As a result, the circle's radius is \[25/\pi \] cm.
Conclusion:
Any 2D shape's perimeter can be calculated by labelling and adding the sides. When calculating the perimeter, don't forget to account for the length of each side. For instance, the lengths of a rectangle's two widthwise edges and its two lengthwise borders are added to form the rectangle's perimeter and similar for other shapes also.
FAQs on Perimeter Of A Figure Explained With Formula And Examples
1. What is the perimeter of a figure?
The perimeter of a figure is the total distance around the outside boundary of a 2D shape. It is found by adding the lengths of all the sides of the figure.
- For polygons, add every side length.
- The answer is always expressed in linear units such as cm, m, or inches.
- Perimeter measures boundary length, not area inside the shape.
2. How do you calculate the perimeter of a shape?
To calculate the perimeter, add the lengths of all the sides of the shape. Follow these steps:
- Step 1: Identify all the outer sides.
- Step 2: Measure or note each side length.
- Step 3: Add all the side lengths together.
3. What is the formula for the perimeter of a rectangle?
The formula for the perimeter of a rectangle is P = 2(l + w), where l is length and w is width.
- Add the length and width.
- Multiply the sum by 2.
4. What is the formula for the perimeter of a square?
The perimeter of a square is calculated using P = 4s, where s is the length of one side.
- Since all sides are equal, multiply one side by 4.
5. How do you find the perimeter of a triangle?
The perimeter of a triangle is the sum of its three side lengths. The formula is P = a + b + c.
- Add the lengths of all three sides.
6. What is the perimeter of a circle called?
The perimeter of a circle is called the circumference. It is calculated using C = 2πr or C = πd, where r is radius and d is diameter.
- Use 2πr if radius is given.
- Use πd if diameter is given.
7. What is the difference between area and perimeter?
The perimeter measures the total boundary length of a shape, while the area measures the space inside it.
- Perimeter is measured in linear units (cm, m).
- Area is measured in square units (cm², m²).
- Perimeter adds sides; area uses specific formulas depending on shape.
8. How do you find the perimeter of an irregular figure?
To find the perimeter of an irregular figure, add the lengths of all its outer sides. Follow these steps:
- Identify every outer edge.
- Measure each side carefully.
- Add all the side lengths together.
9. What units are used to measure perimeter?
The perimeter is measured in linear units such as millimeters (mm), centimeters (cm), meters (m), or inches.
- Use the same unit for all side lengths before adding.
- Convert units if necessary (e.g., 100 cm = 1 m).
10. Can you give an example of finding the perimeter of a figure?
Yes, you can find the perimeter by adding all outer sides of a figure. Example with a rectangle:
- Length = 10 cm
- Width = 6 cm
- Use formula P = 2(l + w)
- P = 2(10 + 6) = 2 × 16 = 32 cm
