Important Formulas: Mensuration | Mathematics (Maths) Class 8 PDF Download

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. 

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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

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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

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Conversion of units 

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