Area - Aptitude Concepts (Important Facts And Formulae)
FUNDEMENTAL CONCEPTS
1.Sum of the all angles of a triangle is 180 degrees.
2.Sum of any two of sides in a triangle is greater than the third side.
3.Pythagoras theorem:
In a right angle triangle,
(Hypotenuse)^2 = (base)^2 + (Height)^2
c^2 = b^2 + a^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 three medians of a triangle meet is called CENTROID of trianlge . Centroid divides each of the medians in the ratio of 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)
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 = 2ΠR.
3. Length of an arc = 2ΠRθ/(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.
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Shubham Prajapati
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