This document discusses various topics in mensuration including the formulas for calculating the area and perimeter of basic shapes like rectangles, parallelograms, trapezoids, triangles, cubes, cuboids, and cylinders. It also covers the concepts of direct and inverse proportion and provides examples. Finally, it discusses the construction of a quadrilateral given specific length measurements of its sides.

1. Made by
Deepak upadhyay

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

4. Rectangle & parallelogram

5. Trapezium & triangle
A Trapezium is a quadrilateral
with one pair of parallel sides
Area of Trapezium = ½×(a +
b)×h
where,
a, b = sides, h = height
Perimeter of Trapezium = a + b
+ c + d
where,
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 = length
b =breadth
a,b and c = sides of the triangle

6. 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
)(2 hrr 

7. 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

8. 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

9. Indirect proportion
Inverse Proportions/Variations
Two 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.

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

11. 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.

15. Made by
Deepak upadhyay