The banking team of jagranjosh.com has come up with concept and sample questions for Mensuration. The concept provided by us will help you to understand the topic. The sample questions offered by us are framed by keeping in view need of the question paper.
Triangles
A figure enclosed by three sides is known as a triangle. A triangle has three angles with total sum of 180^{} and sum of its any two sides is more than the third side.
Equilateral Triangle
It has all three sides equal.
(i) Area =
(ii) Height =
(iii) Perimeter = 3a
Where, a = side, each angle = 60^{}
Isosceles Triangle
It has any two sides and two angles equal and altitude bisects the base.
(i) Area =
(ii) Height =
(iii) Perimeter = a + a + b = 2a + b
Where, a= each of two equal sides
b= third side
Scalene Triangle
It has three unequal sides.
(i) Area
Where, and a, b and c are the sides of the triangle.
(iii) Perimeter = a + b + c
Right Angled Triangle
It is a triangle with one angle is equal to 90^{}
(i) Area
(ii) Perimeter = p + b + h
(iii) h^{2} = p^{2} + b^{2} (Pythagoras theorem)
where, p = perpendicular, b = base and h = hypotenuse
Triangle with Height h
This is a triangle with three unequal sides having certain height.
(i) Area
(ii) Perimeter = a + b + c
Parallelogram
It is a quadrilateral with opposite sides parallel and equal.
(i) Area = Base × Height = b × h
(ii) Perimeter = 2(a + b)
Trapezium
It is quadrilateral with anyone pair of opposite sides parallel.
Area (Sum of the parallel sides × Height)
Where, a and b are parallel sides and h is the height or perpendicular distance between a and b.
Rhombus
It is a parallelogram with all 4 sides equal. The opposite angle in a rhombus are equal but they are not right angle.
(i) Area
(ii) Side
(iii) Perimeter = 4a
(iv)
Where, a = side, d_{1} and d_{2} are diagonals.
Rectangle
(i) Area = Length × Breadth = l × b
(ii) Perimeter = 2(l + b)
(iii) Diagonal
(iv) Area of 4 walls of rectangular room
= 2 × (l + b × h)
Where, l = length, b = breadth, h = height
Square
It is a parallelogram with all 4 sides equal and each angle is equal to 90^{}.
(i) Area
(ii) Perimeter = 4 × side = 4a
(iii) Diagonal
Where, a = side, d = diagonal
Regular Polygon
If each side of a regular polygon of n sides = a
Then,
(i) Area of regular pentagon
(ii) Area of regular hexagon
(iii) Area of regular octagon
(iv) Each exterior angle
(v) Each interior angle = 180^{} – Exterior angle
(vi) Number of diagonals
Circles
It is a plane figure enclosed by a line on which every point is equally distant form a fixed point (centre) inside the curve.
(i) Area = πr^{2}
(ii) Circumference (perimeter) = 2πr
(iii) Diameter = 2r
(iv) Length of the arc
(v) Area of sector
where, r = radius
and
Incase of circular ring,
(i) Area
(ii) Difference in circumference of both the rings
where, R = radius of bigger ring
and r = radius of smaller ring