24 CHAP - 24 .AREA FUNDEMENTAL CONCEPTS I.RESULTS ON...

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24 .AREA FUNDEMENTAL CONCEPTS I.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 . 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. II.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 I .1.Area of a rectangle=(length*breadth) Therefore length = (area/breadth) and breadth=(area/length) 2.Perimeter of a rectangle = 2*(length+breadth) II .Area of a square = (side)^2 =1/2(diagonal)^2 III Area of four walls of a room = 2*(length + breadth)*(height)
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IV 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 V. 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 VI 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. VII . 1. Area of a semi-circle = (pi)*R^2. 2. Circumference of a semi-circle = (pi)*R. SOLVED EXAMPLES Ex.1. One side of a rectangular field is 15 m and one of its diagonals is 17 m. Find the area of the field. Sol . Other side = ((17) 2 - (15) 2)(1/2 ) = (289- 225) (1/2) = (64) (1/2) = 8 m. Area = (15 x 8) m
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24 CHAP - 24 .AREA FUNDEMENTAL CONCEPTS I.RESULTS ON...

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