Key formulas for 2D and 3D mensuration

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

(Unlock A.I Detailed Solution for FREE)

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Here is a comprehensive list of the key formulas for 2D and 3D mensuration, essential for solving geometry problems.

2D Mensuration Formulas (Area and Perimeter)

Square:
- Area = side²
- Perimeter = 4 × side
Rectangle:
- Area = length × breadth
- Perimeter = 2 × (length + breadth)
Circle:
- Area = πr² (where 'r' is the radius)
- Circumference (Perimeter) = 2πr
Triangle:
- Area = (1/2) × base × height
- Perimeter = sum of all three sides
Trapezium (Trapezoid):
- Area = (1/2) × (sum of parallel sides) × height
Rhombus:
- Area = (1/2) × d₁ × d₂ (where 'd₁' and 'd₂' are the diagonals)
- Area = base × height

3D Mensuration Formulas (Surface Area and Volume)

Cube:
- Volume = side³
- Curved Surface Area (CSA) = 4 × side²
- Total Surface Area (TSA) = 6 × side²
Cuboid:
- Volume = length × breadth × height
- Curved Surface Area (CSA) = 2 × h × (l + b)
- Total Surface Area (TSA) = 2 × (lb + bh + lh)
Cylinder:
- Volume = πr²h
- Curved Surface Area (CSA) = 2πrh
- Total Surface Area (TSA) = 2πr(r + h)
Cone:
- Slant Height (l) = √(r² + h²)
- Volume = (1/3)πr²h
- Curved Surface Area (CSA) = πrl
- Total Surface Area (TSA) = πr(r + l)
Sphere:
- Volume = (4/3)πr³
- Surface Area = 4πr²