Perimeter and Area Concepts and Problem Solving

For a two-dimensional figure, perimeter refers to the boundary or path around a shape. On the other hand, the area of a two-dimensional figure is the space occupied within the surface of a shape. There are various types of shapes, but the common ones are square, rectangle, triangle, circle, etc. In this content, you will be able to know the perimeter and area of basic shapes.

Let’s start!

1. Rectangle

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A rectangle is a shape whose opposite sides are equal, and all the angles are right angles (90 degrees).

Perimeter of rectangle = \[2 ( a + b )\]

Area of rectangle = \[ a \times b \]

2. Square

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A square is a shape whose all four sides are equal, and all the angles are 90 degrees.

Perimeter of square = \[ 4 \times a \]

Area of square = \[ a^{2} \]

3. Circle

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A circle refers to a round shape that contains no edges or corners.

Perimeter of circle = \[2 \pi r\] (r = radius)

Area of circle = \[ \pi r^{2} \]

Note: Here the value of pi is either \[\frac{22}{7} \] or 3.14. You can use any one of them if not mentioned in the question.

4. Triangle

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A triangle is a shape with three angles and three straight lines. Triangles can be classified into three kinds, such as:

1. Equilateral Triangle

Perimeter of equilateral triangle = 3 a

Area of equilateral triangle = \[ \frac{1}{4} \times \sqrt{3} \times a^{2} \]

2. Isosceles Triangle

Perimeter of isosceles triangle = 2s + b

Area of isosceles triangle = \[\frac{1}{2} \times\] b \[\times\] hb 

3. Scalene Triangle

Perimeter of scalene triangle = a + b + c

Area of scalene triangle = \[\frac{1}{2} \times b \times h \]

5. Parallelogram

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This shape is a quadrilateral whose opposite sides are parallel.

Perimeter of parallelogram = \[2 ( a + b ) \]

Area of parallelogram = \[b \times  h\]

6. Rhombus

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It is a parallelogram whose sides are equal.

Area of rhombus = \[a \times h \]

Perimeter of Rhombus = \[4 \times a \]

7. Trapezoid

This shape is a quadrilateral which has a minimum of 1 pair of parallel sides.

Perimeter of trapezoid = \[a_1 + a_2 + b_1 + b_2 \]

Area of trapezoid = \[(\frac{( a1 + a2 )}{2}) \times h \]

8. Regular N-Gon

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A regular polygon refers to a polygon whose number of sides and angles are the same.

Area of regular n-gon = \[\frac{1}{2} \times ( a \times n \times s) \]

Perimeter of Regular n-gon = \[n \times s \]

Here are some illustrative examples you can go through to understand the solving procedure.

Ex 1. A rectangular field has length 12 m and breadth 10 m. What will be the area as well as the perimeter of that field?

Solution. Length of the rectangular field = 12 m

Breadth of the rectangular field = 10 m

Therefore, area of the field =\[ l \times b = 12 \times 10 = 120 m^2\]

And perimeter = \[2 ( l + b ) = 2 ( 10 + 12 ) = 44 m\]

Ex 2. Find the perimeter of circles whose radius are (i) 14cm (ii) 10m and (iii) 4km.

Solution. 

1. According to the formula \[ 2 \pi r = 2 \times 3.14 \times 14 cm = 87.92 cm \]

2. \[ 2 \pi r = 2 \times 3.14 \times 10 m = 62.8 m \]

3. \[ 2 \pi r = 2 \times 3.14 \times 4 km = 25.12 km \]

Ex 3. If a rhombus has base and height 10 cm and 7 cm respectively, calculate its area.

Solution. With regards to the question base = 6 cm

Height = 8 cm

Therefore, the area of rhombus = \[b \times h\]

= \[10 \times 7 cm^{2} \]

= \[70 cm^{2} \]

This material is mainly for students who belong to standard VII, so here only the basic formulas are provided. There are some other methods also to solve perimeter and area specifically for shapes like rhombus, triangles, etc. which you will learn in higher classes. 

If you want to refer to other solved examples of area and perimeter numerical, download the Vedantu app today.