NCERT Class 9 MathematicsHerons Formula (Mensuration) Board Sample Problems (For CBSE, ICSE, IAS, NET, NRA 2022)

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Mensuration

It is branch of mathematics which is concerned about the measurement of length, area and Volume of plane and Solid figure

Perimeter

The perimeter of plane figure is defined as the length of the boundary

It units is same as that of length i.e.. m, cm, km

The Perimeter of Plane Figure is Defined as the Length of the Boundary
1 Meter10 Decimeter100 centimeter
1 Decimeter10 centimeter100 millimeter
1 Km10 Hectometer100 Decameter
1 Decameter10 meter1000 centimeter

Area

The area of the plane figure is the surface enclosed by its boundary

It unit is square of length unit. i.e..

The Area of the Plane Figure is the Surface Enclosed by Its Boundary
1 square Meter100 square Decimeter10000 square centimeter
1 square Decimeter100 square centimeter10000 square millimeter
1 Hectare100 square Decameter10000 square meter
1 square myraimeter100 square kilometer square meter

Perimeter and Area of different figure

Perimeter and Area of Different Figure
NShapePerimeter/heightArea
1Right angle triangle Base = b, Height = h Hypotenuse = dP

Height = h

2Isosceles right angled triangle Equal side = a

Height = a

3Any triangle of sides a , b, c

Where

This is called Heron՚s formula (sometimes called Hero՚s formula) is named after Hero of Alexandria

4Square Side = a
5Rectangle of Length and breath L and B respectively
6Parallelograms Two sides are given as a and b

When the diagonal is also given, say d

Then

Where

7Rhombus Diagonal and are given

8Quadrilateral

(a) All the sides are

(b) Both the diagonal are perpendicular to each other

(c) When a diagonal and perpendicular to diagonal are given

(a) P (a)

Where

(b)

where and are the diagonal

(c)

where d is diagonal and and are perpendicular to that