The circumference of a circle can be explained as follows: If you take a thread or a string and curve it around so as to form a circle, then the circumference of the circle is the length of the straightened string.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.
2-D figures (Area and Perimeter)
Area: Area of a 2-dimensional surface is the extent covered by it enclosed within a boundary. Perimeter: Perimeter is the length of the line enclosing a surface. It is the sum of all sides for a polygon. The perimeter of a circle is called its circumference.
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.
- Area of a triangle when base and height are given: (refer fig.1)
A (△) = 1 x b x h 2
- 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
- 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
- Area of an equilateral triangle (refer to fig.5)
A (△) = √3 x a2 4
- Area of an isosceles triangle (refer fig.6)
A (△) = c x √ 4a2-c2 4
- 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|
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 d1 x d2 x sin θ where d1 and d2 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 = side2 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 d1 x d2 where d1 and d2 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
Area of a circle = π r2 Circumference of circle = 2πr
3-D Figures (Volume and Surface area)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
|Cube||a3||TSA = 6a2 LSA = 4a2|
|Cuboid||l x b x h||TSA = 2(lb + lh + bh) LSA= 2(l + b)h|
|Cylinder||πr2h||CSA = 2πrh TSA = 2πr( r + h)|
|Cone||1/3πr2h||CSA = πrl TSA = πr2 + πrl|
|Hemisphere||2/3πr3||CSA = 3πr2|