Made byDeepak upadhyay

Mensuration

Mensuration is the branch of mathematics which deals with the study of Geometric shapes, their area, volume and related parameters.

Rectangle & parallelogram

A rectangle is defined as a quadrilateral where all four of its angles are right angles.

A rectangle  is also a parallelogram

Area of Parallelogram = b×hPerimeter of Parallelogram = 2(b) + 2(h)where,b = breadth, h = height

Area of Rectangle = b*hPerimeter of Rectangle = 2(b) + 2(h)where,b = base, h = heigth

Trapezium & triangle

A Trapezium is a quadrilateral with one pair of parallel sidesArea of Trapezium = ½×(a + b)×hwhere,a, b = sides, h = heightPerimeter of Trapezium = a + b + c + dwhere,a, b, c, d = sides

A triangle is a plane figure with straight sides and three angles Area of triangle: [ l×b /2 ]Perimeter of Triangle: [ (a + b + c) ]Area of Equilateral Triangle: [ (Sqrt (3)/4)×(side)² ]Area of Triangle SAS (2sides & opposite angle): [ ½×a×b×SinC ]Where,l = lengthb =breadtha,b and c = sides of the triangle

SURFACE AREA OF CUBE,CUBOID,CYLINDER Cube – A cuboid whose length ,breadth, and height are equal is called a cube Surface Area of Cube = 6a²

Cuboid - a cuboid is a convex polyhedron bounded by six quadrilateral faces, whose polyhedral graph is the same as that of a cube.Surface area= 2(lb+bh+hl)

Cylinder-is one of the most basic curvilinear geometric shapes, the surface formed by the points at a fixed distance from a given line segment, the axis of the cylinder. Surface area )(2 hrr

Volume of cube,cuboid,cylinder

Volume of a Cylinder

A cylinder with radius r units and height h units has volume of V cubic units given by

Volume of a cube = side times side times side. Since each side of a square is the same, it can simply be the length of one side cubed

V=a3The volume is found using the formula: Volume = Length × Width × Height. Which is usually shortened to: V = l × w × h.

DIRECT & INDIRECT PROPORTION

Two values x and y are directly proportional to each other when the ratio x : y or   is a constant (i.e. always remains the same). This would mean that x and y will either increase together or decrease together by an amount that would not change the ratio.Knowing that the ratio does not change allows you to form an equation to find the value of an unknown variable, for example:

If two pencils cost $1.50, how many pencils can you buy with $9.00?The number of pencils is directly proportional to the cost.    pencils

Direct proportion-

Indirect proportion

Inverse Proportions/VariationsTwo values x and y are inversely proportional to each other when their product xy is a constant (always remains the same). This means that when x increases y will decrease, and vice versa, by an amount such that xy remains the same.Knowing that the product does not change also allows you to form an equation to find the value of an unknown variable for example:

It takes 4 men 6 hours to repair a road. How long will it take 8 men to do the job if they work at the same rate?The number of men is inversely proportional to the time taken to do the job.   hours.

PRACTICAL GEOMETRY

Practical geometry is formed for making figures and constructing it is very important concept in this we shall learn about constructing quadrilateral

Constructing a quadrilateral • when four side and one diagonal are given• When two diagonal and three sides are given• When two adjacent sides and three angle are given• When three sides and two included angles are given

when four side and one diagonal are given Construct a quadrilateral PQRS where PQ = 4 cm,QR = 6 cm, RS = 5 cm, PS = 5.5 cm and PR = 7 cm.Sol: A rough sketch will help us in visualizing the quadrilateral.

When two diagonal and three sides are given

(i) Quadrilateral ABCDab = 4cmac = 8 cmad= 5 cmbc = 6 cmcd = 5.5 cm

When two adjacent sides and three angle are given

(i) Quadrilateral MOREMO = 6 cmOR = 4.5 cm∠M = 60°∠O = 105°∠R = 105°

When three sides and two included angles are given

Construct a quadrilateral LMNO

∠ M=120 ° ∠ N=90 °

MN = 6 cmNY=8cmML=cm

Made byDeepak upadhyay