Perimeter and Area
Perimeter and Area Formulas for All Shapes
For a twodimensional figure, perimeter refers to the boundary or path around a shape. On the other hand, the area of a twodimensional 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!

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 x b

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 x a
Area of square = a^{2}

Circle
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A circle refers to a round shape that contains no edges or corners.
Perimeter of circle = 2 π r (r = radius)
Area of circle = π r2
Note: Here value of pi is either 22/7 or 3.14. You can use any one of them if not mentioned in the question.

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:

Equilateral Triangle
Perimeter of equilateral triangle = 3 a
Area of equilateral triangle = 1/4 x √3 x a^{2}

Isosceles Triangle
Perimeter of isosceles triangle = 2s + b
Area of isosceles triangle = b x hb / 2

Scalene Triangle
Perimeter of scalene triangle = a + b + c
Area of scalene triangle = 1 / 2 x b x h

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 x h

Rhombus
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It is a parallelogram whose sides are equal.
Area of rhombus = a x h
Perimeter of Rhombus = 4 x a

Trapezoid
This shape is a quadrilateral which has a minimum of 1 pair of parallel sides.
Perimeter of trapezoid = a1 + a2 + b1 + b2
Area of trapezoid = (( a1 + a2 )/2) x h

Regular ngon
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A regular polygon refers to a polygon whose number of sides and angles are same.
Area of regular ngon = 1/2 x ( a x n x s)
Perimeter of Regular ngon = n x 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 x b = 12 x 10 = 120 m2
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. (i) According to the formula 2 π r = 2 x 3.14 x 14 cm = 87.92 cm
(ii) 2 π r = 2 x 3.14 x 10 m = 62.8 m
(iii) 2 π r = 2 x 3.14 x 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 x h
= 10 x 7 cm2
= 70 cm2
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 rhombus, triangles, etc. which you will learn in higher classes.
1. Why are area and perimeter important?
Ans. Perimeter and area are the physical aspects of maths, and that is the reason why they are essential. Also, they are the base for comprehending other geometrical aspects like mathematical theorems and volume that helps everyone to understand trigonometry, algebra and calculus.
In everyday life, perimeter and area are used for many purposes, including measuring plots, fencing an area. Some other examples are when engineers plan to construct a house or a swimming pool, farming, covering rooms with carpet, etc.
2. What will be the area of a square park with a perimeter of 320 m?
Ans. Given the shape of the park is a square.
Perimeter of the park = 320 m
Therefore, the length of each side = 320/4 m
= 80 m
So, the area of the park will be = (length of sides)^{2}
= 80 x 80 m^{2}
= 6400 m^{2}
3. How to find a rhombus area by diagonals?
Ans. First, draw a rhombus, ABCD, which have two diagonals AC and BD. The next step is to determine the length of 1st diagonal which is equivalent to the distance from A to C.
Similarly, for the 2nd diagonal, evaluate its length which is the distance from B to D. Remember that rhombus’s diagonals are perpendicular to one another, which makes four 90degree angles when intersecting each other at the middle of rhombus. Then multiply the diagonals d1 and d2 and divide it by 2.