MyMaths MyLife

cube and cuboid:

Consider the fallowing objects: a brick, a box of matches, a die, a text book, a room in the house. They have a common shape, though their sizes are different. The geometrical name that we give to each of these objects is the cuboid.
It has six rectangular faces. There are in all 12 edges of the cuboid. A cuboid has 8 corners called vertices.
The total area of all the six faces of a cuboid is called the total surface area of the cuboid.
Let l,b, and h, be the length, the breadth and the height of a cuboid,
then the lateral surface area= 2h(l+b)

The total surface area
=(the lateral surface area)+(area of ABCD)+(area of EFGH)
=2h(l+b)+lb+lb
=2lh+2bh+2lb
=2(lb+bh+hl)

Area of the four walls of a room:

If we look around and observe the walls of a room, we find that generally the walls are in the shape of a rectangle the floor and the ceiling of the room are also of rectangular shape.
Let l, b, h be the lengths of AB,AD and AE as shown in the figure. Here l and b are the length and breadth of the floor and h the height of the room.
For the rectangle ABFE, the lengths of two adjacent sides are l and h. its area = lh
For the rectangle BCGF, the lengths of two adjacent sides are b and h. its area = bh
For the rectangle CDHG, the lengths of two adjacent sides are l and h. its area = lh
For the rectangle DAEH, the lengths of two adjacent sides are b and h. its area = bh
Observe the opposite walls being of the same size and shape have the same area too.

Hence the total area of the four walls = lh+bh+lh+bh
= 2lh+2bh
= 2h(l+b)

mensuration :Areas

* The area of simple closed figure is the measure of the region closed by the boundary of the figure.

* The area is measured in square units. A square meter is the area of square whose side is one meter.

* A square centimeter is the area of square whose side is one centimeter.

* If l and b denote the length and breadth of a rectangle and A its area, then A=l*b=lb

* If s denotes the side of a square and A its area, then A=s^2.

Important Facts and Formulae:

Results On Triangle

1.Sum of the angles of a triangle is 180 degrees.

2.The sum of any two sides of a triangle is greater
than 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 the MEDIAN.

5.The point where the three medians of a triangle meet,
is called CENTROID. The centroid divides 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.

Results On Quadrilaterals

1.The diagonals of a Parallelogram bisect 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 he parallelogram of given sides the parallelogram
which is a rectangle has the greatest area.




Formulae:

1.Area of a RECTANGLE = length * breadth

Length = (Area/Breadth) and Breadth = (Area/Length)

2.Perimeter of a RECTANGLE = 2(Length + Breadth)

3.Area of a SQUARE = (side)2 = ½ ( Diagonal)2

4.Area of four walls of a room = 2(length + breadth) * height

5.Area of a TRIANGLE = ½ * base * height

6.Area of a TRIANGLE = √[s * (s-a) * (s-b) * (s-c)],
where a,b,c are the sides of the triangle and s = 1/2(a+b+c)

7.Area of EQUILATERAL TRIANGLE = √(3/4)* (side)2

8.Radius of in circle of an EQUILATERAL TRIANGLE of
side a = r / 2√3

9.Radius of circumcircle of an EQUILATERAL TRIANGLE
of side a = r / √3

10.Radius of incircle of a triangle of area ∆ and
semi perimeter S = ∆ / s

11.Area of a PARALLELOGRAM = (base * height)

12.Area of RHOMBUS = 1/2 (product of diagonals)

13.Area of TRAPEZIUM =
=1/2 * (sum of parallel sides)* (distance between them)

14.Area of a CIRCLE =  r2 where r is the radius

15.Circumference of a CIRCLE = 2r

16.Length of an arc = 2 rø / 360, where ø is central angle

17.Area of a SECTOR = ½ (arc * r) = r2ø / 360

18.Area of a SEMICIRCLE = r2 / 2

19.Circumference of a SEMICIRCLE = r