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NCERT Class 8 Mathematics Chapter 11 Mensuration CBSE Board Sample Problems

Mensuration

Mensuration, Perimeter, Area
Sr. noTermDescription
1.MensurationIt is branch of mathematics which is concerned about the measurement of length, area and Volume of plane and solid figure.
2.PerimeterThe perimeter of plane figure is defined as the length of the boundary

It units is same as that of length i.e.. m, cm, km

3.AreaThe area of the plane figure is the surface enclosed by its boundary

It unit is square of length unit. i.e..

Shapes Where Area and Perimeter Are Known

Shapes Where Area and Perimeter Are Known
ShapesperimeterArea
Rectangle
Illustration: Shapes Where Area and Perimeter Are Known
P = 2 (L + B)

L and B are Length and Breadth of the rectangle

Square
Illustration: Shapes Where Area and Perimeter Are Known
P = 4 a

A is side of the square

Triangle
Illustration: Shapes Where Area and Perimeter Are Known
P = sum of sides
Parallelogram
Illustration: Shapes Where Area and Perimeter Are Known
P = 2 (sum of adjacent sides)
Circle
Illustration: Shapes Where Area and Perimeter Are Known

r is the radius of the circle

Trapezium
Illustration: Shapes Where Area and Perimeter Are Known
P = sum of length of all the sides

Half the product of the sum of the lengths of parallel sides and the perpendicular distance between them gives the area of trapezium

General Quadrilaterals
Illustration: Shapes Where Area and Perimeter Are Known
P = sum of length of all the sides
RhombusP = 4 a

Where d1 and d2 are the diagonals of the Rhombus.

Important Terms to remember in case of solid figures

Important Terms to Remember in Case of Solid Figures
Surface AreaSurface Area of a solid is the sum of the areas of its faces
Lateral Surface AreaThe faces excluding the top and bottom make the later Surface Area of the solid
VolumeAmount of space occupied by a three dimensional object (solid figure) is called its volume.

We use square units to find the area of a two dimensional region. In case of volume we will use cubic unit to find the volume of a solid, as cube is the most convenient solid shape (just as square is the most convenient shape to measure area of a region)

Volume is sometimes refer s capacity also

Surface Area and Volume of Cube and Cuboid

Illustration: Surface Area and Volume of Cube and Cuboid
Type and Measurement
TypeMeasurement
Surface area of cuboid of length L, Breadth B and Height H
Lateral Surface Area of the cuboids
Diagonal of the cuboids
Volume of a cuboidsLBH
Length of all 12 edges of the cuboids
Surface Area of cube of side L
Lateral Surface Area of the cube
Diagonal of the cube
Volume of a cube

Surface Area and volume of Right circular cylinder

Illustration: Surface Area and Volume of Cube and Cuboid
Surface Area and Volume of Right Circular Cylinder
RadiusThe radius (r) of the circular base is called the radius of the cylinder
HeightThe length of the axis of the cylinder is called the height (h) of the cylinder
Lateral surfaceThe curved surface joining the two base of a right circular cylinder is called lateral surface.
Type and Measurement
TypeMeasurement
Curved or lateral Surface Area of cylinder
Total Surface Area of cylinder
Volume of cylinder