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Geometry Formulas for All Competitive Exams

Important Formulas of Geometry

Geometry is a wing of mathematics. In geometry, we deal with objects of different shapes and sizes and try to calculate the required values from the given data. Geometry is a combination of two words Geo which means Earth and Metron mean measurement. It is not today’s practice as we measure length, Area and volume very often in our regular life.

Geometry can be divided into two types: Plane Geometry and Solid Geometry. Plane Geometry is the geometry of two-dimensional objects and deals with shapes such as circles, triangles, rectangles, squares, Trapeziums and many more flat shapes. Whereas, Solid Geometry is the geometry of three-dimensional objects such as cubes, cuboids, cylinders, spheres, cones and many related geometrical shapes and structures.

In competitive exams, the general concern of all most all students is the Aptitude and in Aptitude, it’s the problems of Geometry. Many candidates even tell that they skip these problems as all Geometric formulas are very complicated. However, there are some basic formulas that we use frequently and many problems require these basic formulas to solve.

Following are some basic but important Formulas of Geometry.

Plane Geometry

This is the Geometry related to flat two dimensional objects. The objects belonging to this category are Circle, Triangle, Rectangle, Square, Parallelogram, Rhombus, etc.

Circle

The circle is a shape where all points of the shape are at a given distance from a given point or centre. The basic formulas related to circles are given in the following table.

Circle

Parameter

Formula

Circumference of a circle 2πr
Area of a circle πr2
ARC (AB) (2πrθ)/360o
Area of Sector AOB (θ/360o) × πr2
(Circle Formula)

Triangle

A triangle is a closed shape polygon made with three vertices. These are of the following types.

Triangle Types

Parameter

Formula

Area of Any Triangle (1/2) × Base × Height
Perimeter of Any Triangle a + b + c
s = Perimeter/2 (a + b + c) / 2
Area of Any Triangle √{s(s-a)(s-b)(s-c)}
Area of Equilateral Triangle (√3/4) × a2
Perimeter of Equilateral Triangle 3 × a
Area of Isosceles Triangle (b/4) × √(4a2 – b2)
In Any Triangle ∠α + ∠β + ∠θ = 180°
Area of the triangle if two sides and the angle between them is given
(refer to Scalene Triangle of the above image)
(1/2) × a × b sinθ
(1/2) × b × c sinα
(1/2) × c × a sinβ
(Triangle Formula)

Rectangle

A rectangle is a quadrilateral with four right angles and Two of the sides are larger than the other two.

Rectangle

Parameter

Formula

Perimeter of rectangle (a+b) × 2
Area of rectangle a × b
Diagonal (d) √(a2 + b2)
(Rectangle Formulas)

Square

a square is a quadrilateral with four right angles and 4 equal sides.

Square

Parameter

Formula

Perimeter of square 4 × a
Area of square (1/2) × d2 × a2
Diagonal (d) √2 × a
(Square Formulas)

Parallelogram

A parallelogram is a simple quadrilateral with two pairs of parallel sides. 

Parallelogram

Parameter

Formula

Area of Parallelogram b × h
(Parallelogram Formulas)

Rhombus

A rhombus is a quadrilateral whose four sides have the same length.

Rhombus

Parameter

Formula

Area of Rhombus a × h
(1/2) × d1 × d2
Sides (a) of a Rhombus (1/2) × √(d1+d2)
(Rhombus Formulas)

Trapezium

A trapezium is a quadrilateral with at least one pair of parallel sides.

Trapezium

Parameter

Formula

Area of Trapezium (1/2) × (a + b) × h
s (m+c+d)/2 ( if :- (a-b)=m )
h (2/m) × √{s(s-m)(s-c)(s-d)}
(Trapezium Formulas)

Cuboid

A cuboid is a polyhedron having six quadrilateral faces.

Cuboid

Parameter

Formula

Volume of a Cuboid l × b × h
√(A1 × A2 × A3)
Total Surface area of a cuboid 2 (l×b + b×h + l×h)
Diagonal of cuboid √(l2 + b2 + h2)
(Cube Formulas)

Cube

A cube is a polyhedron having six square faces.

Cube

Parameter

Formula

Volume of a cube a3
Total Surface Area 6 × a2
Diagonal of a Cube √3 × a
(Cube Formulas)

Cylinder

A cylinder is a three-dimensional solid that holds two parallel circular bases joined by a curved surface having same cross-section from one end to the other.

Cylinder

Parameter

Formula

Volume of a Cylinder πr2h
Curved Surface Area of a Cylinder 2πrh
Total Surface Area of a Cylinder 2πr2 + 2πrh
(Cylinder Formulas)

Sphere

A sphere is a three-dimensional round-shaped object where every point on the surface is the same distance from the centre.

Sphere

Parameter

Formula

Volume of a Sphere (4/3) × πr3
Surface area of a Sphere 4πr2
Volume of a Hemisphere (2/3) × πr3
Curved surface area of a Hemisphere 2πr2
Total Surface area of Hemisphere 3πr2
(Sphere Formulas)

Right Circular Cone

A Right Circular Cone is a three-dimensional solid that holds a circular base and an equidistance point from the circumference of the circle.

Right Circular Cone

Parameter

Formula

Slant Height (s) of a Right Circular Cone √(h2 + r2)
Volume of the Right Circular Cone (1/3) × πr2h
Curved Surface area of Right Circular Cone πrs
(Right Circular Cone Formulas)

Frustum of Right Circular Cone

A cutting section parallels to the base but not passing through the vertex of a cone portion forms the Frustum of a Right Circular Cone.

Frustum of Right Circular Cone

Parameter

Formula

Volume of the Frustum of Right Circular Cone (πh/3) × (r2 + R2 + Rr)
Slant Height (s) of Frustum of Right Circular Cone √{h2 + (R – r)2}
Curved Surface Area of Frustum of Right Circular Cone π(r+R)s
Total Surface Area of Frustum of Right Circular Cone π{(r + R)s + r2 + R2}
(Frustum Formulas)

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