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Area - Facts & Formulae
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I.FACTS ON TRIANGLES:
Sum of the angles of a triangle is 180 degrees.
Sum of any two sides of a triangle is greater than the third side.
In a right angle triangle,
(Hypotenuse)^2 = (base)^2 + (Height)^2
The line joining the midpoint of a side of a triangle to the opposite vertex is called the MEDIAN
The point where the three medians of a triangle meet is called CENTROID.
Centroid divides each of the medians in the ratio 2:1.
In an isosceles triangle, the altitude from the vertex bi-sects the base
The median of a triangle divides it into two triangles of the same area.
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.FACTS ON QUADRILATERALS:
The diagonals of a parallelogram bisects each other .
Each diagonal of a parallelogram divides it into two triangles of the same area
The diagonals of a rectangle are equal and bisect each other.
The diagonals of a square are equal and bisect each other at right angles.
The diagonals of a rhombus are unequal and bisect each other at right angles.
A parallelogram and a rectangle on the same base and between the same parallels are equal in area.
Of all the parallelograms of a given sides , the parallelogram which is a rectangle has the greatest area.
.Area of a rectangle=(length*breadth)
Therefore length = (area/breadth) and breadth=(area/length)
Perimeter of a rectangle = 2*(length+breadth)
Area of a square = (side)
Area of four walls of a room = 2*(length + breadth)*(height)
Area of the triangle=1/2(base*height)
Area of a triangle = √
where a,b,c are the sides of a triangle and s= ½(a+b+c)
Area of the equilateral triangle =√
Radius of circle of an equilateral triangle of side a = a/2 √
Radius of circumcircle of an equilateral triangle of side a = a / √
Radius of circle of a triangle of area del and semi perimeter S=del/S
Area of the parlelogram =(base *height)
Area of the rhombus = ½(product of the diagonals)
Area of the trapezium = ½(size of parallel sides)*distance between them
Area of a circle =∏*r
,where r is the radius
Circumference of a circle = 2*∏*R.
Length of an arc = 2∏*R* é/(360) where é is the central angle
Area of a sector = (½) (arc x R) = ∏*R^2*é/360. where é is the central angle
Area of a semi-circle = (∏)*R
Circumference of a semi-circle = (∏)*R.
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