NCERT / CBSE NOTES : Chapter Summary


Mensuration

Methods to Find Area of Quadrilaterals and Polygons:

We can find the area of the triangle using the formula   
To find the area of a quadrilateral we will divide the quadrilateral into two triangles and add the areas of the two triangles.

Triangulation

The method of dividing a quadrilateral into two triangles to find out its area is known as triangulation.

Let ABCD is a quadrilateral. Then
Area of quadrilateral ABCD 
= (Area of ∆ ABD) + (Area of ∆ BCD)
= ½ d (), where d is the diagonal and  and  are the heights of the quadrilateral.
Area of quadrilateral ABCD= ½ d ()
triangulation, quadrilateral, area of a quadrilateral
In a parallelogram the diagonal divide it into two triangles. Now

Area of a Parallelogram = base × height
parallelogram, Area of a Parallelogram

Rhombus 

In a rhombus diagonals are perpendicular to each other, so we can use the method of triangulation to find the area of a rhombus
Area of a Rhombus =  (), where  and  are the lengths of the diagonals.
triangulation, rhombus, area of a rhombus
Area of a Rhombus =  (), where  and  are the lengths of the diagonals.

Trapezium 

trapezium has a pair of parallel sides.

Area of trapezium =  
Where h = perpendicular distance between the parallel sides of a trapezium and a and b are the lengths of the parallel sides.
Area of trapezium = 
trapezium, Area of trapezium

Polygon 

polygon is a closed shape that has at least three sides. It is a closed shape that has at least three sides. Triangles, quadrilaterals, rectangles and squares are all types of polygons. Moreover, a polygon can be of any shape and can have any number of sides. There is no specific formula for calculating the area of a polygon. The best way is to split the polygon into shapes whose area can be calculated individually.

polygon, area of a polygon
polygon, area of a polygon

Surface Area of Solids

Cube: A cube is a three-dimensional figure, a solid made up of six equal squares called faces.
cube, LSA, lateral surface area, surface area, lateral faces

The lateral surface area (LSA) of a cube is equal to 4l2, whereas its total surface area (TSA) is 6l2.

Cuboid: A cuboid is a solid made up of six rectangles, called faces. The total area of a cuboid is the sum of the areas of these faces.
cuboid, lateral surface area, total surface area, total surface area of a cuboid, lateral surface area of a cuboid
The lateral surface area (LSA) of a cuboid is 2h (l + b), whereas its total surface area (TSA) is (lb + bh + hl).

Cylinder:
A cylinder is a solid composed of two congruent circles in parallel planes.

curved surface area, cylinder, total surface area of a cylinder, curved surface area of cylinder, total surface area

The curved surface area (CSA) of a cylinderical pillar is 2πrh , whereas its total surface area (TSA) is  2πr(r+ h).
curved surface area, cylinder, total surface area of a cylinder, curved surface area of cylinder, total surface area

Volume of Solids

Bodies that occupy space are called solids.
Solid bodies occur in various shapes, such as cuboid, cube, cylinder and cone.
The space occupied by a solid body is called its volume.
The units for volume are cubic centimetre(cm3), cubic metre(m3) etc.
solids, space, volume, units of volume
A cuboid is a solid bounded by six rectangular plane faces.
Consider a cuboid of length, breadth and height , and , respectively. Then:
  • Volume of cuboid = lbh cubic units
  • Total surface area of cuboid = 2(lb + bh + lh)sq.units
  • Lateral surface area of cuboid = Area of 4 walls = Area of 4 walls = 2h(l + b)sq.units
cuboid, volume of a cuboid,  total surface area of a cuboid, lateral surface area of a cuboid, area of four walls
A cube whose length, breadth and height are all equal is called a cube.
Consider a cube of edge a units. Then:
  • Volume of cube = a3 cubic units
  • Total surface area of cube = 6a2 sq.units
  • Lateral surface area of cube = 4a2 sq.units
cube, volume of a cube,  total surface area of a cube, lateral surface area of a cube
A solid bounded by a cylindrical surface and two parallel circular bases at the top and bottom is called a cylinder.
Consider a cylinder of radius r units and height h units. Then:
  • Volume of cylinder 
  • Total surface area of cylinder 
  • Lateral surface area of cylinder 
The volume of a cylinder is also sometimes known as its capacity.

Post a Comment Blogger

 
Top