Area - Important Formulae

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:
      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 FORMULAE

1. 1.   Area of a rectangle = (Length x Breadth).

   Length =		Area		and Breadth =		Area		.
   		Breadth				Length

   2.   Perimeter of a rectangle = 2(Length + Breadth).
2. Area of a square = (side)² = (diagonal)².
3. Area of 4 walls of a room = 2 (Length + Breadth) x Height.
4. 1.   Area of a triangle =  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 = (a + b + c).

   3.   Area of an equilateral triangle =	3	x (side)2.
   	4

   4.   Radius of incircle of an equilateral triangle of side a =	a	.
   	23

   5.   Radius of circumcircle of an equilateral triangle of side a =	a	.
   	3

   6.   Radius of incircle of a triangle of area  and semi-perimeter s =
   	s

5. 1.   Area of parallelogram = (Base x Height).
   2.   Area of a rhombus =  x (Product of diagonals).
   3.   Area of a trapezium =  x (sum of parallel sides) x distance between them.
6. 1.   Area of a circle = R², where R is the radius.
   2.   Circumference of a circle = 2R.

   3.   Length of an arc =	2R	, where  is the central angle.
   	360

   4.   Area of a sector =	1	(arc x R)	=	R2	.
   	2			360

7. 1.   Circumference of a semi-circle = R.

   2.   Area of semi-circle =	R2	.
   	2

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