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Area

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 opposite vertex is called themedian.
    5. The point where the three medians of a triangle meet, is calledcentroid.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)
    wherea,b,care the sides of the triangle ands=(a+b+c).
    3. Area of an equilateral triangle = 3 x (side)2.
    4
    4. Radius of incircle of an equilateral triangle of sidea= a .
    23
    5. Radius of circumcircle of an equilateral triangle of sidea= a .
    3
    6. Radius of incircle of a triangle of areaand semi-perimeterr= .
    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 , whereis 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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