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^{0} 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^{0}

**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^{0}

(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**

- It is a parallelogram with equal opposite sides and each angle is equal to 90
^{0}.

(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^{0}.

(i) Area

(ii) Perimeter = 4 × side = 4a

(iii) Diagonal

Where, a = side, d = diagonal

**Regular Polygon**

- In regular polygons, all sides and all interior angles are equal. A polygon is called pentagon, hexagon, heptagon, octagon, nanogon and decagon according as it contains 5, 6, 7, 8, 9 and 10 sides respectively.

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^{0} – 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