Area and Perimeter


Perimeter

A perimeter means the distance of the boundary of a two-dimensional shape. Also, it is defined as the sum of the length of all the sides of the object. The algebraic sum of the length of each side is the perimeter of that shape. 

Perimeter is the measurement of the total length of the sides of a given shape or polygon when we want to measure the perimeter of a polygon all we need to do is to add the length of all its sides. We have formulas available for the various shapes in geometry.

परिमाप शब्द दो शब्दो से मिलकर बना है – परि और माप। अर्थात किसी आकृति के सभी भुजाओं के माप को परिमाप (Perimeter) कहते हैं। जैसे- आयत का परिमाप उसकी चारों भुजाओं के योग के बराबर होता है; वर्ग का परिमाप उसकी भुजा का चार गुना होता है; आदि। हम किसी भी आकृति का परिमाप उसके सभी भुजाओं की लम्बाई को जोड़कर ज्ञात कर सकते है।

Below are the formulas for perimeter of different 2d shapes.

Geometric ShapePerimeter FormulaMetrics
Parallelogram2(Base + Height)
Trianglea + b + ca, b and c being the side lengths
Rectangle2(Length + Width)
Square4aa =Length of a side
Trapezoida + b + c + da, b, c, d being the sides of the trapezoid
Kite2a + 2ba = Length of the first pair
b = Length of the second pair
Rhombus4 x aa  = Length of a side
Hexagon6 x aa  = Length of a side

Area

While area can be defined as the region covered by a flat shape or the surface of an object the area of figure in the number of unit squares that a group at the surface of a closed figure.

क्षेत्रफल: किसी समतल आकृति द्वारा घेरा जाने वाला स्थान अथवा आकृति की सीमाओं के अंदर के धरातल का परिमाप, उसका क्षेत्रफल कहलाता है। क्षेत्रफल का मात्रक ‘वर्ग इकाई’ होता है।

साधारण भाषा में कहें तो एरिया से आप समझ सकते हैं कि किसी सतह को रंगने में कितने पेंट की जरूरत पड़ेगी वही उसका एरिया है। 

मान लीजिए कि किसी दीवार को रंगने में 1 लीटर पेंट की जरूरत पड़ती है और किसी दूसरी दीवार को रंगने में 2 लीटर पेंट की जरूरत पड़ती है तो फिर दूसरी दीवार का एरिया पहली दीवार के एरिया से दुगना होगा।

Area of 2D Shapes Formula

In general, the area of shapes can be defined as the amount of paint required to cover the surface with a single coat. Following are the ways to calculate area based on the number of sides that exist in the shape, as illustrated below in the fig.

Area Of Shapes

Let us write the formulas for all the different types of shapes in a tabular form.

Shape AreaTerms
Circleπ × r2r = radius of the circle
Triangle½ × b × hb = baseh = height
Squarea2a = length of side
Rectangle l × wl = lengthw = width
Parallelogramb × hb=baseh=vertical height
Trapezium½(a+b) × ha and b are the length of parallel sidesh = height
Ellipseπaba = ½ minor axisb = ½ major axis

Perimeter = Sum of all sides

=> Perimeter = 3cm+5cm+3cm+5cm

=> Perimeter = 16cm

Area = Total number of unit squares

=> Area(of rectangle)= length (l) X breath(b)

=> Area(of rectangle) =5cm X 3cm

=> Area=15 cm sq


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