Geometry is great fun when you have all the geometrical formulas on your fingertips. This ScienceStruck article provides a complete printable list of geometrical formulas.
When it comes to the subject of geometry, it mainly includes the nature of shapes, how to define them, and what we are taught in relation to the world at large. Learning geometry is actually knowing the core of everything that exists on Earth, including you. We outline the formulas in geometry that are pretty simple to memorize. * Click anywhere on the article to obtain a print.
- Area of a triangle when base and height are given: (refer fig.1)
A (△) = 1 x b x h 2 A (△) = Area of Triangle b = Base h = Height
- Area of a triangle when all 3 sides are given: (refer fig.2)
A (△)=√ s(s-a)(s-b)(s-c), where s is the semiperimeter and a, b, c are the sides of the triangle. Perimeter of a triangle= a+b+c If s is the semiperimeter,
s = a+b+c 2
- When 2 sides and the angle between them is known, (refer to fig.2)
A(△) = 1 x a x b x SinC 2 A(△) = 1 x b x c x SinA 2 A(△) = 1 x a x c x SinB 2 Where, A △ = Area of Triangle a, b, c are the sides, SinA, SinB, SinC = are the sines of the corresponding angles between the sides
- Area of a triangle when inradius is given (refer fig.3) A=r x s where r=inradius and s=semiperimeter
- Area of a triangle when circumradius is given, (refer fig.4)
A (△) = a x b x c 4R where a, b, c are sides of the triangle and R is the circumradius
- Area of an equilateral triangle (refer to fig.5)
A (△) = √3 x a^{2} 4 where a is the side of the equilateral triangle
- Area of an isosceles triangle (refer fig.6)
A (△) = c x √ 4a^{2}-c^{2} 4 Where a is the length of 2 equal sides and c is the length of third side.
- Area of a right-angled triangle (refer to fig.7) A (△) =½ x (product of perpendicular sides)
A polygon is a geometrical figure which is closed and has more than 2 straight sides. A polygon with: 3 sides is known as a triangle, 4 sides is known as a quadrilateral, 5 sides is known as a pentagon, 6 sides is known as a hexagon, 7 sides is known as a heptagon, 8 sides is known as a octagon, 9 sides is known as a nonagon, 10 sides is known as a decagon. For a Regular Polygon with n sides: Sum of all interior angles = (n-2) x 180º How to find value of one angle of a regular polygon when number of its sides are given?
Value of one angle of a regular polygon = | (n-2)x180º |
n |
Value of interior angle + value of exterior angle = 180º Area of a regular polygon = ½ x (perimeter) x (perpendicular from center to any side) Perimeter of a polygon= sum of all sides of the polygon.
If all vertices of a polygon lie on a circle, then that polygon is called a cyclic polygon.
Sum of all the 4 angles of a quadrilateral = 360º Area of a quadrilateral = ½ x (diagonal) x (sum of perpendicular from the opposite vertices) Area of a quadrilateral= ½ x d_{1} x d_{2} x sin θ where d_{1} and d_{2} are the diagonals and θ is the angle between them.
Area of a parallelogram = base x altitude
Area of a rhombus = ½ x product of diagonals
Area of a square = side^{2} Area of a square= ½ x (diagonal)^{2} Perimeter = 4 x side
Area of a rectangle = length x breadth Perimeter = 2 x (length + breadth)
Area of a trapezium = ½ x (sum of parallel sides) x height
Area of a kite = ½ x d_{1} x d_{2} where d_{1} and d_{2} are diagonals
Area of a cyclic quadrilateral = √ (s-a)(s-b)(s-c)(s-d) where s is the semiperimeter and a, b, c, d are the sides of the cyclic quadrilateral
s = | a+b+c+d |
2 |
Area of a circle = π r^{2} Circumference of circle = 2πr
Volume: 3-dimensional figures occupy some space. Volume is a measure of this space occupied by them. Volume can also said to be the space contained within a 3-dimensional figure. Surface Area: The amount of paper required to cover the 3-dimensional figure entirely is its surface area. If a figure has curved surfaces, its surface area is called curved surface area. Total surface area is the sum of flat surface area and curved surface area. In the following table: Diag. stands for diagram Vol. stands for volume SA stands for Surface area LSA stands for lateral surface area CSA stands for curved surface area TSA stands for total surface area
3D Figure | Diag. | Vol. | SA |
Cube | a^{3} | TSA = 6a^{2} LSA = 4a^{2} | |
Cuboid | l x b x h | TSA = 2(lb + lh + bh) LSA= 2(l + b)h | |
Sphere | 4/3πr^{3} | CSA= 4πr^{2} | |
Cylinder | πr^{2}h | CSA = 2πrh TSA = 2πr( r + h) | |
Cone | 1/3πr^{2}h | CSA = πrl TSA = πr^{2} + πrl | |
Hemisphere | 2/3πr^{3} | CSA = 3πr^{2} |