AREA

RESULTS ON TRIANGLES:

1. Sum of  the angles of a triangle is 180 degrees.
2. Sum of any two sides of a triangle is greater than the third side.
3. Pythagoras theorem:
• In a right angle triangle,
• (Hypotenuse)^2 = (base)^2 + (Height)^2
4. The line joining the midpoint of a side of a triangle to the opposite vertex is called the MEDIAN
5. The point where the three medians of a triangle meet is called CENTROID.
1. Centroid divides each of the medians in the ratio 2:1.
6. In an isosceles triangle, the altitude from the vertex bi-sects the base
7. The median of a triangle divides it into two triangles of the same area.
8. Area of a triangle formed by joining the midpoints of the sides of a given triangle is one-fourth of the area of the given triangle.

RESULTS ON QUADRILATERALS:

1. The diagonals of a parallelogram bisects each other .
2. Each diagonal of a parallelogram divides it into two 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 parallelograms of a given sides , the parallelogram which is a rectangle  has the greatest area.

IMPORTANT FORMULAE

1. Area of a rectangle=(length*breadth)
1. Therefore length = (area/breadth) and breadth=(area/length)
2. Perimeter of a rectangle = 2*(length+breadth)
2. Area of a square = (side)^2 =1/2(diagonal)^2
3.  Area of four walls of a room = 2*(length + breadth)*(height)
4. Area of the triangle
1.  Area of the triangle=1/2(base*height)
2.  Area of a triangle = (s*(s-a)(s-b)(s-c))^(1/2), where a,b,c are the sides of a triangle                   and s= ½(a+b+c)
3.  Area of the equilateral triangle =((3^1/2)/4)*(side)^2
4.  Radius of incircle of an equilateral triangle  of side a=a/2(3^1/2)
5.  Radius of circumcircle of an equilateral triangle of side a=a/(3^1/2)
6.  Radius of incircle of a triangle of area del and semiperimeter S=del/S
5. Area of the parellogram
1. Area of the parellogram =(base *height)
2. Area of the rhombus=1/2(product of the diagonals)
3. Area of the trapezium=1/2(size of parallel sides)*distance between them
6. Area of a circle
1. Area of a circle =pi*r^2,where r is the radius
2. Circumference of a circle = 2∏R.
3. Length of an arc = 2∏Rθ/(360) where θ is the central angle
4. Area of a sector = (1/2) (arc x R) = pi*R^2*θ/360.
7. Area of a semi-circle
1. Area of a semi-circle = (pi)*R^2.
2. Circumference of a semi-circle = (pi)*R.