Dear Readers,

Today in this post, we are providing you remaining part of the necessary formula and concepts related to Geometry and Mensuration from the Quant section.

Today in this post, we are providing you remaining part of the necessary formula and concepts related to Geometry and Mensuration from the Quant section.

**TRIANGLES :**Triangles are closed figures containing three angles and three sides.

**General Properties of Triangles:**

The sum of the two sides is greater than the third side: a + b > c, a + c > b, b + c > a

**Area of a Triangle:**

**•**

**Area of a triangle =**

**1/2 x base x height=1/2 x a x h**

**•**

**Area of a triangle= 1/2 bcsinA = 1/2ab sinC=1/2 acsinB**

**•**

**Area of a triangle = abc/4R where R circumradius**

**•**

**Area of a triangle= r x s where r inradius and s = (a+b+c)/2**

**REGULAR POLYGONS : **A regular polygon is a polygon with all its sides equal and all its interior angles equal. All vertices of a regular lie on a circle whose center is the center of the polygon.

**•**

**Each interior angle of a regular polygon = 180(n-2)/n**

**•**

**Sum of all the angles of a regular polygon = n x180(n- 2)/n = 180(n-2).**

**Quadrilateral:**A quadrilateral is any closed shape that has four sides. The sum of the measures of the angles is 360°. Some of the known quadrilaterals are square, rectangle, trapezium, parallelogram and rhombus.

**Square:**A square is regular quadrilateral that has four right angles and parallel sides. The sides of a

square meet at right angles. The diagonals also bisect each other perpendicularly.

If the side of the square is a, then its

**•**

**Perimeter = 4a,**

**•Area = a^2**and the length of the

**diagonal = √2a**

**Rectangle:**A rectangle is a parallelogram with all its angles equal to right angles.

**•**

**Area of a rectangle = length × breadth**

**•**

**Perimeter = 2(sum of length and breath)**

**Parallelogram:**A parallelogram is a quadrangle in which opposite sides are equal and parallel.

Any two opposite sides of a parallelogram are called bases, a distance between them is called a height.

**•**

**Area of a parallelogram = base × height**

**•**

**Perimeter = 2(sum of two consecutive sides)**

**Rhombus:**If all sides of parallelogram are equal, then this parallelogram is called a rhombus.

**•**

**Area of a rhombus = 1/2 product of diagonals**

**•**

**Perimeter = 4a,**

**Trapezoid:**Trapezoid is a quadrangle two opposite sides of which are parallel.

**•****Area of a trapezoid = 1/2(Sum of parallel sides)height**

**CIRCLE:**A circle is a set of all points in a plane that lie at a constant distance from a fixed point. The fixed point is called the center of the circle and the constant distance is known as the radius of the circle.

**Arc: **An arc is a curved line that is part of the circumference of a circle. A minor arc is an arc less than the semicircle and a major arc is an arc greater than the semicircle.

**Chord:**A chord is a line segment within a circle that touches 2 points on the circle.

**Diameter:**The longest distance from one end of a circle to the other is known as the diameter. It is

equal to twice the radius.

**Circumference:**The perimeter of the circle is called the circumference.

**•**

**circumference = 2πr,**where r is the radius of the circle.

**•**

**Area of a circle: Area = π x (radius)^2 = πr^2.**

**Sector:**A sector is like a slice of pie (a circular wedge).

**Area of Circle Sector: (with central angle θ) Area = θ/360 xπ x r^2**

**Length of a Circular Arc: (with central angle θ) The length of the arc = θ/360 x2π x r**

**Tangent of circle:**A line perpendicular to the radius that touches ONLY one point on the circle

**Cuboid:**A parallelepiped whose faces are rectangular is called a cuboid. The three dimensions

associated with a cuboid are its length, breadth and height (denoted as l, b and h here.)

**• The total surface area of the cuboid = 2(lb + bh + hl)**

**• Volume of a cuboid = lbh**

**Cube:**A cube is a parallelepiped all of whose faces are squares.

**•****Total surface area of the cube = 6a^2**

**• Volume of the cube = a^3**

**Right Circular Cylinder:**A right circular cylinder is a right prism whose base is a circle. the cylinder has a base of radius r and a height of length h.

**•****Curved surface area of the cylinder = 2πrh**

**• Total surface area of the cylinder = 2πrh + 2πr^2**

**• Volume of the cylinder = πr^2h**

**Right Circular Cone:**a right circular cone is a pyramid whose base is a circle. In , the right circular cone has a base of radius r and a height of length h.

**•**

**Curved surface area of the cone = πrl**

**• Total surface area of the cone = πrl + πr^2**

**• Volume of the cone =1/3πr^2h**

**Sphere:**A sphere is a set of all points in space which are at a fixed distance from a given point. The fixed point is called the centre of the sphere, and the fixed distance is the radius of the sphere.

**•**

**Surface area of a sphere = 4πr^2**

**• Volume of a sphere = 4/3πr^3**

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