Feedback
Home
Fundamental Concepts
 
  1. Results on Triangles:
    1. Sum of the angles of a triangle is 180°.
    2. The sum of any two sides of a triangle is greater than the third side.
    3. Pythagoras Theorem:
      4. In a right-angled triangle, (Hypotenuse)2 = (Base)2 + (Height)2.
    4. The line joining the mid-point of a side of a triangle to the positive vertex is called the median.
    5. The point where the three medians of a triangle meet, is called centroid. The centroid divided each of the medians in the ratio 2 : 1.
    6. In an isosceles triangle, the altitude from the vertex bisects the base.
    7. The median of a triangle divides it into two triangles of the same area.
    8. The area of the triangle formed by joining the mid-points of the sides of a given triangle is one-fourth of the area of the given triangle.
  2. Results on Quadrilaterals:
    1. The diagonals of a parallelogram bisect each other.
    2. Each diagonal of a parallelogram divides it into triangles of the same area.
    3. The diagonals of a rectangle are equal and bisect each other.
    4. The diagonals of a square are equal and bisect each other at right angles.
    5. The diagonals of a rhombus are unequal and bisect each other at right angles.
    6. A parallelogram and a rectangle on the same base and between the same parallels are equal in area.
    7. Of all the parallelogram of given sides, the parallelogram which is a rectangle has the greatest area.
Important Formulas
I.
1.   Area of a rectangle = (Length x Breadth).    
 
 
 
  Length =  
Area
Breadth
  and Breadth =  
Area
Breadth
  .      
 
2.   Perimeter of a rectangle = 2(Length + Breadth).    
   
II.
  Area of a square = (side)2 =
1
2
 (diagonal)2  
   
III.
  Area of 4 walls of a room = 2 (Length + Breadth) x Height.    
   
IV.
1.   Area of a triangle =
1
2
 x Base x Height.
 
2.   Area of a triangle = s(s-a)(s-b)(s-c)  
 
    where a, b, c are the sides of the triangle and s =
1
2
 (a + b + c).
 
3.   Area of an equilateral triangle =
3
4
 x (side)2
 
4.   Radius of incircle of an equilateral triangle of side a =
a
2 3
 
 
5.   Radius of circumcircle of an equilateral triangle of side a =
a
2 3
 
 
6.   Radius of incircle of a triangle of area and semi-perimeter s =
2 3
 
   
V.
1.   Area of parallelogram = (Base x Height).  
 
2.   Area of a rhombus =
1
2
 x (Product of diagonals).      
 
3.   Area of a trapezium =
1
2
 x (sum of parallel sides) x distance between them.      
   
VI.
1.   Area of a circle =
R2, where R is the radius.
 
2.   Circumference of a circle = 2
R
 
3.   Length of an arc =
2
R
360
 , where
 is the central angle.    
 
4.   Area of a sector =
1
2
 (arc x R) =
R2
360
     
   
VII.
1.   Circumference of a semi-circle =
R
 
2.   Area of semi-circle =
R2  
2
   
   
 
  © 2024 infibee.com. All Rights Reserved.   Copyright | Privacy Policy | Sitemap  
Contact us on : info@infibee.com  
 
 
Share   Facebook   Twitter   Google +   Digg