Area and Perimeter are two important properties of two- dimensional shapes. Perimeter is defined as the distance of the boundaries of the shape whereas Area explains the region occupied by it. This article will help you improve your knowledge regarding the concept of finding areas and perimeters for different figures. To make this easy for you we have observed the step-by-step solutions for all the questions.

This will be applicable for any shape and size, whether it is regular or irregular. Each and every shape has its own area and perimeter formula. You will learn about different shapes such as triangle, square, rectangle, circle, sphere, etc. The area and perimeter of plane figures or shapes are discussed here.

Also, Read:

### Area and Perimeter – Definitions

**Area:** Measurement of the plane region is called Area, a part of the plane is enclosed by a simple closed figure is called a plane region. It is measured in square units.

**Perimeter:** The closed figure’s length of the boundaries is called the Perimeter of the plane figure. The units of Perimeter are the same as that of length that is m, cm, m, mm, and etc.

### Perimeter and Area of Plane Figures Formulas

The different plane figures Area and Perimeter formulas are discussed below. The plane figures are circle, square, rectangle, triangle, pentagon, and Hexagon.

**Perimeter and Area of a Square: **

The perimeter of a square is 4a.

Let ‘a’ be the length of the sides of a square.

The area of a square is a x a = a².

The length of the diagonal is 2a.

The diagonal of a square is a√2.

**Perimeter and Area of a Rectangle:**

The perimeter of a rectangle is 2(l+b).

So l is the length of the rectangle and b is the breadth of the rectangle.

The area of a rectangle is length x breadth.

The diagonal of the rectangle is √(l² +b²).

The length of the diagonal is l² +b².

**Perimeter and Area of a Circle:**

The area of a circle is πr².

The Circumference of a circle is 2πr, which is equal to πd.

We know that the value of π is 3.14 or π = 22/7.

r is the radius of the circle.

d is the diameter of the circle.

The area of the ring is,

Area of the outer circle – Area of the inner circle.

**Perimeter and Area of a Triangle:**

The area of a triangle is 1/2 (base x height).

The length of the sides is a, b, c. The area of a triangle is s(a+b+c)/2.

The perimeter of a triangle is (a+b+c).

**Area of Parallelogram:**

The area of a parallelogram is Base x Height (Product of base and height).

**Area of a Trapezium:**

The area of a trapezium is (1/2)(Sum of all parallel sides) x Height.

The different plane figures perimeter and area formulae are given in the below tabular form:

### Perimeter and Area of Plane Figures Questions

**Problem 1:**

The Length of a rectangular field is 23.7 m and the breadth of its field is 14.5 m respectively.

Find the following,

(i) What is the barbed required wire to fence the field?

(ii) Area of the field.

**Solution:**

As given in the question the data,

Now, we have to find the solutions to the given questions.

The length of a rectangular field is 23.7 m

The breadth of a rectangular field is 14.5 m

So, the following are

(i) Barbed wire required for fencing the field = perimeter of the field

= 2 (length + breadth)

= 2(23.7m + 14.5m) = 76.4 m

(ii) The Area of the field is, length × breadth

= 23.7 × 14.5 m. square

= 343.65 m. square

**Problem 2:**

On a square-shaped handkerchief, nine circular designs, each of radius 7 cm, are made. What is the area of the remaining portion of the handkerchief?

**Solution:
**In the given question,

As the radius of each circular design is 7 cm.

The diameter of each will be 2 × 7 cm = 14 cm

So, the side of the square handkerchief is 3 × 14 cm = 42 cm

Therefore, the area of the square is 42 × 42 cm²

Also, the area of a circle = πr² = 22/7 x 7 x 7 cm² = 154 cm².

Thus, the area of 9 circles is 9 × 154 cm².

Next, the area of the remaining portion of the handkerchief is,

= (42 × 42 – 9 × 154) cm²

= (1764 cm² – 1386 cm²) = 378 cm².

Hence, the area of the remaining portion of the handkerchief is 378 cm².

**Problem 3:**

If the radius of a circle is 20cm. Find its area and circumference?

**Solution:
**Given the data, the radius of a circle is 20 cm.

Now, we will find the area and circumference of the circle.

So, the area of a circle is π × r².

A= 22/7 x 20 x 20

A= 1257.14 sq.cm.

The circumference of the circle is, C=2πr

C= 2 x 22/7 x 20 = 125.7 cm

Thus, the area and circumference of a circle are 1257.14 sq. cm, 125.7 cm.

**Problem 4:**

If the length of the side of a square is 12cm. Find the area of a square and also find the total length of its boundary?

**Solution:
**Given in the question,

The length of the side of a square is a = 12 cm.

Now, we need to find the area and total length of its boundary.

So, the area is a² = 12² = 144 sq.cm

Next, we will find out the total length of its boundary is,

Perimeter = 4a = 4 x 12 = 48 sq.cm.

Hence the area and total length of the boundary are 144 sq. cm and 48 sq. cm.

### FAQ’s on Perimeter and Area of Plane Figures

**1. What is the difference between area and perimeter?**

The area is the region covered by shape or figure and the units of the area are square units or units² whereas the perimeter is the distance covered by the outer boundary of the shape and the units of the perimeter are the same as the unit.

**2. What is the formula for Perimeter?**

The perimeter of any polygon is equal to the sum of its all sides.

Perimeter = Sum of all sides.

**3. What is the formula for the area of the rectangle? **

The area of the rectangle is equal to the product of its length and breadth (l x b).

So, the area of the rectangle is length x breadth.

**4. What is the area and perimeter of a circle?**

A circle is a curved shape and its area and perimeter are given by its radius.

So, the area of a circle is πr².

Now, the Perimeter or circumference of a circle is 2πr.