Important Formulas Mensuration - (Maths) Class 8

Terms

1. Mensuration

It is branch of mathematics which is concerned about the measurement of length, area and Volume of plane and Solid figure

2. Perimeter

• The 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. Area

• The area of the plane figure is the surface enclosed by its boundary
• It unit is square of length unit. i.e. m² ,  km²

Shapes where Area and Perimeter are known

1. Rectangle

• Perimeter: P= 2(L+B)
  L and B are Length and Breadth of the   rectangle 
• Area: A = L × B 

2. Square

• Perimeter: P=4a
  a is the side of the square
• Area: A = a²

3. Triangle

• Perimeter: P=Sum of sides
• Area: A=(1/2)×(Base)×(Height/Altitude)

4. Parallelogram

• Perimeter: P=2(Sum of Adjacent sides) 
• Area: A=(Base) ×(Height)

5. Circle

• Perimeter: P=2πr
  r is the radius of the circle
• Area: A=πr²

6. Trapezium

• Perimeter: P= Sum of length of all the sides 
• Area: A=(1/2)h( a+b)
  Half the product of the sum of the lengths of parallel sides and the perpendicular distance between them gives the area of trapezium

7. General Quadrilaterals

• Perimeter: P= Sum of length of all the sides 
• Area: A=(1/2)d(h₁+ h₂)

8. Rhombus

• Perimeter: P=4a
• Area: A= (1/2)×d₁ × d₂
  Where d₁ and d₂ are the diagonals of the Rhombus. 

Important Terms to remember in case of Solid Figures

Surface Area and Volume of Cube and Cuboid

1. Surface Area of Cuboid of Length L, Breadth B and Height H 

• Measurement: 2(LB + BH + LH).

2. Lateral surface area of the cuboids

• Measurement: 2( L + B ) H

3. Diagonal of the cuboids

• Measurement:

4. Volume of a cuboids

• Measurement: LBH

5. Length of all 12 edges of the cuboids

• Measurement: 4 (L+B+H).

6. Surface Area of Cube of side L

• Measurement: 6L²

^{7. Lateral surface area of the cube}

• Measurement: 4L²

^{8. Diagonal of the cube}

• Measurement: L√3

9. Volume of a cube

• Measurement: L³

Surface Area and Volume of Right circular cylinder

• Radius: The radius (r) of the circular base is called the radius of the cylinder.
• Height: The length of the axis of the cylinder is called the height (h) of the cylinder.
• Lateral Surface: The curved surface joining the two base of a right circular cylinder is called Lateral Surface.

1.  Curved or lateral Surface Area of cylinder

• Measurement: 2πrh

2. Total surface area of cylinder

• Measurement:2πr (h+r)

3. Volume of Cylinder

• Measurement: π r²h

Conversion of units 

1. 1 cm³ = 1 mL
2.  1L = 1000 cm³
3. 1 m³ = 1000000 cm³ = 1000L